sethoflagos

That's not what I said at all. I said that you persistently confuse actual machine efficiency with the Carnot limit. However, hot surfaces transmit more momentum than cold surfaces. So although it is entirely possible for a cold body to transmit a quantum of heat to a hot body, it is overwhelmed by the momentum flow in the opposite direction. The nett direction of heat flow is determined by force of numbers.

Okay, let's try and work our way through this step by step. No it wouldn't. 100% of the enthalpy of the hot working fluid is thermodynamically available for conversion to work, but all real machines have their inefficiencies. So in practice, you may only recover, say, 80% of this as nett work output. We would call this figure the isentropic efficiency of the machine (as opposed to the thermal efficiency). The remaining 20% of the energy input would be discharged to the cold sink with the working fluid at a significantly higher temperature than the cold sink. I've underlined that last part because it is crucially important. It's where the excess entropy is being generated. This is were we need to be extremely careful about which efficiency were are talking about - the theoretical Carnot limit or the real world isentropic efficiency. In the theoretical world there could be a near zero heat flow into a cold sink at absolute zero. In the real world, there would be a significant heat flow. .Only for a machine with an isentropic efficiency of 100% which is not a practical proposition. For a real world machine impeding the heat exchange is equivalent to heating up the cold sink. Less of the input energy is now available for conversion to work. The two scenarios are not equivalent. In fact they are polar opposites. Absolutely not. They are diametrically opposed. From the extreme difference in temperatures on the cold side of the machine. Correct. The work produced is limited by the isentropic efficiency. Reread my first point in this post. You're conflating the Carnot limit with actual machine isentropic efficiency. They are entirely different concepts. Confusing the two leads to absurd conclusions especially at absolute zero. Again focus on the phrase 'maximum efficiency'. Can we agree that this is different from 'actual efficiency'? Here you are allocating an isentropic efficiency of 100% to the machine. I'm finding it difficult to picture 4% of the output of a typical hair dryer as a 'massive heat transfer' and indeed how one would see it. I see no science here. You've gone a long way down a rabbit hole and need to find your way back. It's taken me quite a while to wade through all the steps in your thinking so I'd be grateful if you spent a similar amount of effort in trying to understand what I've presented here. Obviously, I'm only too happy to assist with further clarification.

Refresh your memory of what a heat engine is at https://en.wikipedia.org/wiki/Heat_engine Other than demonstrate that industrial machines are tested by professionals up to their thermodynamic limits on a daily basis contrary to your claims.

And yet your engine still runs. Therefore there is still a significant thermal gradient across the device. Because they have significant losses over an ideal isentropic process. In addition to the usual friction losses, they feature approximately isothermal expansion and compression stages that are a lot less efficient than the corresponding approximately adiabatic stages employed in turbines for example; mixing of warm and cold working fluid occurs around and through the displacer piston; and the kinetic energy of your aforementioned convection currents has to come from somewhere.

You are not reducing the cold side overall heat transfer coefficient as much as you think you are. The machine as supplied is designed to run despite the cold side heat rejection passing through two 'insulators': acrylic and air. Adding a layer of aerogel only retards convection. The machine clearly is able to run on 'conduction only' mode. So aerogel is just a different type of air as far as the machine is concerned. Designs of this type do not approach the Carnot limit in any way shape or form so trying to draw any conclusions about the validity of Carnot efficiency is kind of crass.

What design of Stirling engine is it? Alpha? Beta? Gamma? Something else? Manufacturer/Model number? Is there a schematic diagram available so we can see the piston arrangement, heat exchangers locations, regerator (if any) just to give us some idea of what you're asking us to comment on. What's the process gas? Hydrogen? Helium? Air?

I thought that you might care to review your claim that information entropy was not subect to 2nd Law constraints after browsing through this paper: https://www.physik.uni-kl.de/eggert/papers/raoul.pdf I've attached a copy for your convenience. Other relevant references are: https://en.wikipedia.org/wiki/Maxwell's_demon https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory I think some of the confusion lies in a tendency to think of information theory in purely abstract, mathematical terms when its application is very much a real world phenomenon. Shannon definitely framed it in terms of a physical link between sender and receiver. In fact there seems to be a growing view that classical Clausius entropy and von Neumann entropy are simply special cases of the more general Shannon entropy. And the 2nd Law rules them all. raoul.pdf Markus, Can you briefly explain why we shouldn't expect to find a quark-gluon plasma at the heart of a black hole. There should be no problem in storing a huge amount of entropy in a small core of that if the uncertainty principle and extreme temperature is sufficient to resist collapse.

I'd say not, but it does rather depend on what you mean by 'state'. A simple example maybe?

Are you sure about this? It sounds very Maxwell's Demonish. In context any perfectly homogenous space carries no Shannon entropy because any measurement you make at any point always returns the same value. The information content is zero. However the moment you discover a 'surprise' anomalous reading, something at that point is in a different state. Not only does that different state imply a different energy but you've acquired and stored the new information. Even if you've managed to acquire the information by reversible means, the stored data must at some point be deleted. As for Shannon entropy having no units, it's entirely reasonable to characterise thermodynamic entropy by quantities like S/R which are also dimensionless.

Several times up until the last glacial maximum https://en.wikipedia.org/wiki/Bab-el-Mandeb had a land bridge crossing. Similarly, the continental shelf under the Strait of Hormuz was exposed at the same time (see https://www.jstor.org/stable/10.1086/657397?seq=4) though there would still be at least one river crossing to make (Tigris and Euphrates have to exit somewhere!)

This is a reference to Ptolemy's celestial spheres that the Islamic world of the time was well acquainted with. See https://en.wikipedia.org/wiki/Celestial_spheres

Well at least that spares me having to point out that 'following the African rains' involves covering ~20 km/day every day. Tough on the kids and old folks.

Are you asking me or telling me?

Curiously boreal concept for a venture that was mainly confined to the tropics/subtropics for 20-30,000 years. Yes, of course, there can be all sorts of reasons to want to move on. And there does seem to be in increased prevalence of alleles associated with risk-taking among migrant groups, though which is cause and which effect is not clear to me. Perhaps some really did enjoy the adventure. Not sure I'd have offered them life insurance policies.

From what I gather, all three of these people were writing around or a little after the fall of the Abbassid Caliphate in Baghdad to the forces of Hulagu Khan in 1258. Could it be possible that their writings were coloured by such tumultuous events occurring around them, while the world centre of scientific learning for the previous 3 or 4 centuries was being laid waste? Rather than trying to find the underlying truth in the imaginations of poets, I'd be more inclined to look at what contemporary scientists were writing at the time. Have you looked at the writings of https://en.wikipedia.org/wiki/Nasir_al-Din_al-Tusi?

Hunter-gathering certainly does include a nomadic element but left to their own devices don't you think such groups would tend to stick to a familiar home range that they understood well rather than risk the uncertainties of moving to an unfamiliar territory. This is long before the age of pastoral nomads or trader nomads, so I'm not sure the word is helpful without qualification.

Different forces are in play with different orders of magnitude through the start up process. When you start rotating the mixing bar, it acts like the impeller of a centrifugal pump and creates a pressure low spot at the 'eye of the pump'. This draws water down past the calcium block while the vortex is developing its parabolic profile above. The calcium rich water is then propelled radially outward until the flow regime is fully established. Now entropy takes over and calcium slowly diffuses up through the water column until it's evenly distributed.

I don't think they migrated because they enjoyed travel. More likely, as their population increased, limited resource availability forced them to expand into new territories.

Sperm heads have to do battle with (for them) substantial hydrodynamic forces, so again that's going to favour a prolate spheroid geometry. (Like little submarines). The major design challenge for organs like testes and ovaries is in keeping the internal plumbing of blood supplies and outgoing products as compact as possible. This favours a more spherical shape to keep pipe runs as short as possible, with maybe a navel or collar at major connection points. Similar challenges as gooseberries, watermelons and garden peas etc.

Neither do I, but compression ratios are still finite and therefore the Bekenstein bounds still limit the amount of information that can be stored in a given space.

So your OP reduces to 'What is the best compression algorithm for big numbers?'.

The earth's surface is almost exactly 2x10^84 square Planck units. I vaguely remember reading that something unpleasant happens when you try storing that much information on a limited surface.

It isn't just a matter of absolute magnitude alone. The largest defined finite integers (such as Graham's number) have a very limited set of prime factors, or are very closely related mathematically to such (eg 10^100 + 1). One can easily envisage integers that are vanishingly small in comparison to Graham's number, but are far more difficult define uniquely due to the complexity of their prime factor composition and hence their mathematical remoteness from our established notational shortcuts. The problem then reduces to finding the smallest integer that cannot be uniquely defined within a computable space. A couple of approaches spring to mind. Say we set an arbitrary bound on our computer processor to 2^64 bit arithmetic operations and addressing. Recognising that our decimal based counting system is itself an abbreviation of the numbers, we can now count in base 2^64 up to 2^64 digits. That system tops out at 18,446,744,073,709,551,616^18,446,744,073,709,551,616 (>10^(19*10^19)) A second approach may be to recognise that all integers may be represented by Producti=1,n (Pi^yi) where Pi is the ith prime number. Setting the same bit-width bounds on n and y, the first number that fails to compute will be the measly 2^2^64 ~ 10^(8*10^19), but since the majority of referable primes will have magnitudes far in excess of 2^64, the number field will extend far beyond this.

How do you square this claim with your speciosity figures for the various orders: Where mammals are in last place as niche holders. Most notably being eclipsed by the extant dinosaurs (birds) that you claim were superseded by mammals? Your vision of a continuous transition to 'a higher level of evolution' far from being 'A New Theory of Evolution' seems to me to be a rebranding of some aspects of Lamarckism. An old theory that has been long debunked. Evolution only lives in the moment and works with the genetic material available to it at the time. It has no long term goals. It is entirely possible that the next mass extinction is survived by nothing more complex than say, lichen. What kind of progess would that be?

You're welcome. Some years ago we went over all this with a fine toothcomb on a trumpeter's forum I drop into from time to time. There was a general concensus in support of Ericsson's conclusions.