sethoflagos

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.

You're paraphrasing the core message of Malcolm Gladwin's 'Outliers: The Story of Success'. Gladwin's background is in journalism. His work heavily borrows from and grossly distorts the work of K. Anders Ericsson, a Swedish Professor of Psychology, particularly his research on deliberate practice as presented in such books as 'Towards a General Theory of Expertise' (1991). This quote from https://en.wikipedia.org/wiki/Practice_(learning_method) highlights a major discrepancy in Gladwin's 'motivational' interpretation: And by 'deliberate practice', the implication is total engagement a highly structured programme of skills development with regular feedback from an expert tutor. Clearly reading a book on the subject would not count as deliberate practice for example.

Mad as a bag of weasels. I've spent most of the last twenty years mentoring Nigerian graduate chemical engineers, both male and female. While there are plenty of gripes on differential terms of employment, I never heard a whisper of any cultural bias in the subject itself other than its innate opacity to the innumerate.

Many compromises are involved. Just considering bird's eggs. Burrowing birds tend to lay nearly spherical eggs which optimises content volume / shell area, or more particularly shell calcium content as a birds calcium reserves tend to be a limiting factor in egg production. This is also the strongest shape for a given calcium budget. Cliff nesting birds tend to lay highly pyriform (pear-shaped) eggs that tend to roll in a tight circle helping to prevent them rolling off the edge and also positioning the air bubble in the egg close to where the oxygen hungry brain and eyes will form. For active fliers, aerodynamic requirements produce a strong adative pressure to form eggs that present a low cross-sectional area against the direction of flight and this favours a more ellipsoidal shape (prolate spheroid to be pedantic). Most species fall in between these three idealised geometries with the balance being optimised for each one's characteristic lifestyle.

Sorry. Caught me on a bad day.

No offence taken, but do you really think my handling of the N-S equations is sub-graduate level? What I was primarily looking for was some help with the differential equations. Essentially, if I can't get Laplace transforms to work I'm stumped on the analytical solutions. I've had more success with numerical methods on the simplest cases, but anything beyond simple (eg the slightest hint of rotational flow) basically needs a Cray with the methodology I've been using.

In putting together maintenance teams, it's common practise to pair up a 'bright spark' with a 'steady Eddie'. One to determine the root cause of the problem, and one to see that it's properly dealt with. Their strength is in their diversity, and I strongly believe similar priciples are true on a broader scale in society as a whole. But above all, I have a profound distrust of those who promote IQ testing, for reasons best summed up in https://en.wikipedia.org/wiki/Buck_v._Bell. (It's still on the statute books).