How many species 3: an answer, and some more questions.

| 51 Comments

In a previous post, I presented an example of one of the questions that evolutionary biologists face. In this example, I described three populations of closely related insects, presented a few details about their distribution, and gave the results for some laboratory-based breeding studies that were conducted with these populations some years back. I then asked people to guess how many species the three populations were divided into by scientists. Their answers, and some questions, can be found in comment threads both at The Panda’s Thumb and at The Questionable Authority.

If you look at the answers that people have given, you will see that all three possible choices (1 species, 2 species, and 3 species) have received some votes. The most popular answer is that there are 2 species, with populations A and B being put together as a single species, and population C being given status as a separate species. The people who have chosen this option focused on the obvious differences in fertility for the crosses involving population C. The person who voted for three species did so based on the high likelihood that all three populations are on separate evolutionary tracks. The people who voted for a single species did so based on the fact that, despite the male sterility, population C is still interfertile with populations A and B. Several people also asked for more information. I’ll try to satisfy some of those requests in this post.

Read More (at The Questionable Authority):

51 Comments

Again, the writer has assumed that a (legitimate) speculative hypothesis is foundational, and is interpreting his observations so that they mould to that foundation. The questioner Karl is a mathematician and if he holds a rational view of Nature he will know that everything natural can ultimately be described in terms of numbers. As Kelvin emphasized, everything that is natural can have a model built to exactly simulate it. The model may be an actual machine or it may be a mathematical description of a real machine. Anything that cannot ultimately be modelled mathematically is by definition supernatural. We have a long way to go with our maths and especially with information technology in nature. If anyone can tell us, for example, exactly how thinking is carried on in a brain - or for that matter, clearly explain to us amateurs how photosynthesis works - you will be doing well. These are natural phenomena, so they can be reduced to concise terms - expressed if need be as numbers. Speciation is likewise a natural phenomenon. It’s complexity may be daunting but nevertheless will be mathematical. Again, as observation, classification, common sense, and the Scriptures confirm, organisms reproduce “after their kind”. The biblical context presumably places the emphasis on organisms visible to the naked eye, although it may well carry through to the microscopic. For the intents and purposes for which it is written, species reproduce the same species, and any two organisms capable of producing viable fertile offspring are the same species. Species are real and definable. Darwin was weak on that point and groundbreaking biologists such as Mendel were strong on it. The observable species are to be used to define any theory of their origin; an origin theory cannot be employed to define the observable species. Some people have got the cart well and truly before the horse. I would comment at THE QUESTIONABLE AUTORITY direct but the login mechanism rejected every login name I entered, which perhaps goes to illustrate that even man made machines act like nature - unpredictably - whilst remaining real, math-based machines.

well this sounds exactly like what a phd project should be trying to disentangle! good luck…

from what i know about the drosophila (which is little) on hawaii there are splitters and lumpers, which is essentially what we’ve gotten from the comments. it’s likely that the island groups all represent close species..but eh.…shrug.….?????

If you want some good answers on the Hawaiian Drosophila, you’ve got a nice local resource out there. Talk to Pat O’Grady - he’s a new Asst. Prof in one or another of the departments out there.

“If you want some good answers on the Hawaiian Drosophila, you’ve got a nice local resource out there. Talk to Pat O’Grady - he’s a new Asst. Prof in one or another of the departments out there.”

I know… he’s in my group. hehe. that’s where i’ve gotten all of my info on hawaiian drospophila.…

do you know the roderick/gillespie crowd?

No, I’m still in the new grad student, trying to make contacts stage of the game. This month, I’m working on getting my field permits. Later on this summer I’ll try to get in touch with Rosie and George. (I don’t know them directly, but if they still have a border collie named Bear, I got mine from the same source.) Right now my only contact with an experienced Hawaiian Drosophila worker is Ken Kaneshiro. My own advisor (Dave Carlon) is pretty good on speciation-related genetics, but his own preferred system is coral. I wanted something a little drier. (It’s also much easier to work with the D. grimshawi complex now that Pat went through all that trouble to get the genome sequenced. ;)

Philip Heywood wrote:

“…if he holds a rational view of Nature he will know that everything natural can ultimately be described in terms of numbers.”

Mathematics is just a language. It is useful to science but like all languages it has limitations.

“…any two organisms capable of producing viable fertile offspring are the same species.”

No. Failure in fertilization is evidence of speciation. There are other isolating mechanisms however, such as behavioural and morphological changes, which can act as isolating mechanisms.

“Species are real and definable.”

Species are conceptual. How ‘real’ they are depends on how you define them.

“Darwin was weak on that point and groundbreaking biologists such as Mendel were strong on it.”

Darwin recognized some of the difficulties in defining species. I don’t think Mendel had anything to say on the subject.

for reproductive isolation issues perhaps a better discussion model would be centrarchid fishes. there are a number of species that are interfertile and hybrid swarms and introgression persist along contact zones and in manmade habitats where multiple species have been stocked. i suppose the issue is similar in the rift lakes and cichlids. regardless the original distributions of species made biogeographic sense, a signal which is still clear despite introductions and fragmentations from impoundments etc. there are general ecological differences between many of these fishes as well. hell, if there is such a thing as a species (a category of entity) they are good species. but they readily interbreed, given the chance. reproductive isolation is a fuzzy context dependent delineation tool.

given that old observer bias issue, and the quantum uncertainty issue, and despite the fact that i can identify a bluegill sunfish from all the other sunfish, i still think that pluralist approaches suggest that species are not ‘real’ in the sense that someone affirmed above. if we conceive of evolution along a time-continuum then they cannot be ‘real’ at all, except in the arbitrary sense of a category we have created. a mathematical formulation of that category does nothing to demolish that issue.

If they are real, then wittgenstein was wrong.

It sounds like you’ve settled on a reproductively isolated breeding population, supported by evidence of ecological, behavioral, and genetic differences between populations as a working definition of a species. If so, it is then a matter of establishing the magnitude of these effects that will qualify a population as a new species.

Do you have convincing threshold values for each of these characteristics?

The Oahu and Kauai populations and D. pullipes will only deposit eggs in the presence of rotting bark from plants of the genus Wickstroemia. The Maui Nui populations will ovideposit virtually anywhere.

Have you explored the biochemistry of Wickstroemia. Since, like D. pullipes, the Oahu and Kauai populations are restricted to plants in this genus, are there unique compounds produced by plants in this genus that are metabolized by Oahu and Kauai populations? Loci encoding these enzymes might show evidence of selection while in Maui Nui populations which can use a variety of plants as hosts the same loci would not be under selection. This could be used as evidence to support your contention to separate out these populations.

Delta Pi Gamma (Scientia et Fermentum)

Hey, Erasmus:

How do you pronounce “cichlids”? I’ve always wanted to know but never heard anyone say it.

Thanks.

“Species” seems to be more like a label than a property.

How do you pronounce “cichlids”? I’ve always wanted to know but never heard anyone say it.

like this:

“sicklid”

Returning to the original question, and including all groups mentioned in this post; I would say there are three species.

The Kauai and Oahu groups obviously represented two isolated populations of a single species. The are reported to have the same appearence, same habitat, same behaviour, and most importantly, to be fully interfertile with each other. If equal numbers of both groups were transferred to a third island which did not already contain members of D. grimshawi, they would quickly interbreed and form a single genetic pool. The relatively deep genetic division between the two is an accident of geography, and has no relevance to their status as members of the same species.

The infertility of males from K/O group crosses with D. pullipes strongly suggests that if members of both were transferred to a third island, within a short time one would entirely supplant the other; or they would diverge in their ecological niche; but that they would not form a single genetic pool. For this reason I would consider them distinct species. This is the same reason I gave for considering the Maui Nui populations a distinct species, and the new data gives me no reason to question that assignment.

Finally, the infertility between K/O populations and Maui Nui populations, though distinctly less than that between either and D. pullipes is probably sufficient that they also ought to be assigned to distinct species.

I am basing my decisions on the criteria that different species are at minimum supposed to be genetically distinct. If we have two distinct groups which we assign as distinct species which later form a common genetic pool, we have made a mistake in our classification. Likewise, if we have two distinct populations which we assign to a single species, which then have an opportunity to interbreed in the wild, but remain as genetically distinct populations, we have also made a mistake in our classification. Consequently, my decision to assign distinct species status depends on my estimate of the probability that the populations will remain distinct if fortuitous circumstance should end their geographical isolation.

Based on this idea, I would want detailed information on some other biological facts before making a firm conclusion. Specifically, as the pace of evolution depends on the variability of traits in a population, and as strong selection for mating prefferences is also (ipso facto) strong selection pressure to break down fertility barriers; I would like to know the variability in fertility outcomes for cross breeding between the populations, along with the variability of traits that might be selected for to form pre-mating barriers against interbreeding. If variability of fertility outcomes was significantly higher variability in possible pre-mating barriers, then I would assign the relevant groups as distinct sub-species rather than distinct species.

For my two cents worth - species are classifications of convenience for slowly moving (evolving) targets. I’m a relativist as far as this goes - determine what the objective of your classification is, and ignore the fuzziness at the boundaries. :-)

“As Kelvin emphasized, everything that is natural can have a model built to exactly simulate it.”

Mathematics can model nature, but the models aren’t nature. No model or theory can describe nature perfectly. Your example of a brain is likely such a case. Chaos is definitely one, you can never exactly reproduce each event even if you intend to.

“Anything that cannot ultimately be modelled mathematically is by definition supernatural.”

The definition of natural comes from observation. The insufficience of modelling mean that it can’t replace the natural (sic!) definition.

“Some people have got the cart well and truly before the horse.”

Oh, the irony!!!

Re “and ignore the fuzziness at the boundaries.”

Yeah, it’s a bit like looking at a tree where one branch splits into two, and trying to draw precise lines between the base and each of the two limbs so as to classify each cell as belonging to one or the other.

Henry

Syntax Error: not well-formed (invalid token) at line 14, column 28, byte 1674 at /usr/local/lib/perl5/site_perl/5.12.3/mach/XML/Parser.pm line 187

Anton Mates Wrote:
Heywood Wrote:

Anything that cannot ultimately be modelled mathematically is by definition supernatural.

I’m a mathematician and I don’t even know what that statement means. Eggs can be described in terms of numbers and ghosts can’t?

I think it’s simple enough. You, Anton, cannot be modeled mathematically, hence you are supernatural. I suppose it’s Dembski’s excuse for assuming that intelligence is supernatural.

Well, fine, we’re all gods, and we can give up science, religion, and anything else we might not wish to subscribe to. ID is an inherently nihilistic set of beliefs.

Glen D http://tinyurl.com/b8ykm

Well, fine, we’re all gods

cool!

I wanna be a naughty god.

If anyone out there is a rain god then we could sure do with you visiting us here in Australia!

OT:

heyo displaced Kiwi:

if you get the chance to contact your mates about the PKI dive stuff, could you shoot me some info. here:

[Enable javascript to see this email address.]

cheers

oh, and I’d love to hear what you are working on over in the thread where we started this OT convo.

I sent a first point of contact for the Leigh Marine Reserve this morning. It should be there, unless hotmail kills emails with urls in them?

I don’t know what Einstein or Stephen Hawkings would comment re. the limitations of mathematics. Mathematics is definitely not my strong point, but I have an impression Einstein struggled with this concept of randomness (is that chaos?) and Hawkings reckons he’s got the physical universe fairly well in the bag, maths - wise, except for gravity. I suspect we might find that maths-physicists have a somewhat more rigorous definition of nature/the physical than do some of us in the descriptive professions. The point I am making regarding species and speciation is that they happened, through real, measurable processes; they are not, if you like, “chaos”; and the way to discover these processes is first and foremost to clear the mind of preconceptions, rely on logic and scientific laws, and make deductions based on unbiased observation. If one doesn’t know how speciation occurred, one shouldn’t be definitively stating that it occurred one way or the other. Quickly or slowly. Certainly there are a few pointers - including, as has been mentioned, divergence within populations. But if you were to try to tell me that speciation simply happens through divergence of populations within species, I would rightly advise you to go and get your thesis showing the actual events involved - not omitting DNA, immune system, and all the other paraphenalia of a species. Something based on mathematically definable processes. And something that meets all the observational criteria - E.G., why it is possible to class a human as a human and not as an ape. Any volunteers?

I sent an E-mail recently to an academic who claims to have the goods when it comes to indoctrinating students on this sort of topic, I advised him of new tchnological developments that tend to show how speciation might have occurred. He replied to the effect that it was all settled, 150yrs ago. That attitude explains exactly why people like AIG are getting more and more kudos. The fruitflies? When the Papuan Fruitfly invaded (fruitfly-infested) North Australia the Primary Industries Department had no trouble specifically identifying and attacking it. There are such things as species. Linnaeus, Mendel, Owen,and the rest of them weren’t altogether daft.

Philip. Yes there are such things as species, because we call them so, placing “like with like”. However they are dynamic not static entities.

Your arguments here are old hat, and are just indicative of your lack of knowledge. Do the research yourself.

As for AIG, they have no credibility in the science world because they try to reinforce a superstitious position through the distortion of facts and presentation of mis- and half-truths.

They also have marginal credibility in mainstream religious thought because of their distorted theology, and because they are a blatant exemplar of everything old Augustine warned good Christians against.

That attitude explains exactly why people like AIG are getting more and more kudos.

BWA HA HA HA HA HA AH AHA HA HA AHA HA HA A !!!!!!

You’re a funny guy, Heywood.

“AIG is getting more and more kudos”.

BWA HA HA HA HA HA AHA HA HA AHA HA HA HA AHA HA !!!!!!

I think you’re right about not being able to model Anton mathematically. Chaos theory might be more applicable?

I sent a first point of contact for the Leigh Marine Reserve this morning. It should be there, unless hotmail kills emails with urls in them?

just received.

thanks.

Chaos theory? Count these others in as well. Lenny, do you need that handkerchief, or are you trying to morph into a donkey?

I think what Lenny is trying to point out, is that unlike PT, which has, in fact, been awarded kudos by several scientific organizations… AIG, has er, well,

NOT.

he’s laughing at you claiming that it has received any meaningful kudos.

get it?

Philip Wrote:

Certainly there are a few pointers - including, as has been mentioned, divergence within populations. But if you were to try to tell me that speciation simply happens through divergence of populations within species, I would rightly advise you to go and get your thesis showing the actual events involved - not omitting DNA, immune system, and all the other paraphenalia of a species. Something based on mathematically definable processes. And something that meets all the observational criteria - E.G., why it is possible to class a human as a human and not as an ape. Any volunteers?

Showing speciation through the divergence of populations was essentially what this series of posts is all about. So far, I’ve presented different levels of hybrid sterility separating different populations, and I’ve mentioned the measured levels of genetic differentiation separating these populations. In addition to the populations I’ve already discussed, there are a number of other closely-related species in the picture-wing clade that show still more differentiation in genetic traits and in reproductive isolation. In fact, while the reproductive isolation measurements are incomplete, the crosses that have been attempted with other picture-wing species show full hybrid sterility, non-viable males and reduced-fertility females, failure of the hybrids to fully mature, failure to advance beyond an early stage of larval development, failure to hatch, and failure to fertilize - that’s pretty much the whole range of possibilities there. I’ll discuss that material more in a post in another day or two.

The geological situation in these islands is such that we can put maximum ages on many of these species, and in geological and evolutionary terms (although not in YEC terms) they are all very young - 5 million years or so is the maximum age, and the youngest taxa are well less than 1 million years old. We can also make a damn good stab at the cause of initial divergence in many cases - dispersal and the founder effect have played a large role in the history of life in Hawaii.

As far as your whole Math focus is concerned, I’d strongly suggest that you take a couple of semesters of population genetics before you comment further on the mathematical poverty of evolutionary biology. As the situation currently stands, you look like a fool.

Philip Heywood Wrote:

I don’t know what Einstein or Stephen Hawkings would comment re. the limitations of mathematics. Mathematics is definitely not my strong point, but I have an impression Einstein struggled with this concept of randomness (is that chaos?)

No; chaos is a deterministic attribute. Basically it just means that tiny changes in starting conditions lead to vast changes in the future behavior of the solution, so that even if the solution is theoretically perfectly predictable, if you wanted to know what it does over a long period of time you would have to measure the initial conditions to an unrealistic level of accuracy.

Biological and ecological systems are of course the very definition of chaos (as well as involving lots of randomness). Your average human being’s future can vary wildly depending on whether or not he’s got a single virus of, say, Ebola somewhere in his body. Likewise the future state of an island continent’s ecosystem could be completely torqued by dropping a single pregnant rat on the beach. Which is why a demand that we model/describe the past history of the Earth or one of its evolutionary lineages “with mathematical precision,” and catalogue every single hypothetical event that occurred along the way, cannot be taken seriously. That’s not a weakness in evolutionary theory–that’s simply how reality is observed to work.

and Hawkings reckons he’s got the physical universe fairly well in the bag, maths - wise, except for gravity.

I…don’t think Stephen Hawking would agree with that.

If one doesn’t know how speciation occurred, one shouldn’t be definitively stating that it occurred one way or the other. Quickly or slowly.

And something that meets all the observational criteria - E.G., why it is possible to class a human as a human and not as an ape. Any volunteers?

By your definition above, it’s not currently possible to claim that humans and other apes are different species; we haven’t done hybridization tests.

we haven’t done hybridization tests.

are you sure about that?

I’ve often thought that the only explanation for some of the banana-mush brained stuff posted by various creobots on PT could best be explained by some sort of human-simian hybrid.

They’re not hybrids. You need to give the apes more credit.

come to think of it, wasn’t there a recent study published that showed chimps were able to deductively reason that paint could color a surface, but not a knife?

that does suggest that simians and apes likely have more deductive reasoning capabilities than shown by most of our resident creobots.

However, how do we know that hybridization wouldn’t produce something with less deductive reasoning capacity than either parent?

… mules for example, are often considered to be more “stubborn” than either parent…

… and you have to twist their noses to get them to move!

hmmm, really?

that gives me an idea to try with the next creobot i speak with in person…

Yeah, they use what I think is called a twitch, a circle of rope that they twist around the upper part of their hooter (nose - not breast).

Could be a good combination with a toejam.

Happy to correspond via email on PKI etc.

Cheers

Lenny, do you need that handkerchief, or are you trying to morph into a donkey?

There’s only one braying jackass here, Heywood.

Sorry to change the subject. It’s intriguing.

I think I made an error above re. fruitfly invasion of nth Aust. I think the invader may have been named something like the Papayan Fruitfly rather than Papuan. Only heard the word, didn’t see it in print. I know nothing about the creature involved and am merely assuming it was a fruitfly, proper. I am enlightened re. chaos - o.k.. Chaos theory as you describe it certainly must have applications in nature. The idea that biological systems are chaotic in the sense of being ultimately unguided is manifestly difficult. Do the probability on things being like they are, beginning with “primordial soup”, or the “big bang”, or whatever one chooses. Start with a mixture of chemicals: end with a microbe. Already the probability requirements have blown out to be approaching infinity. That’s one reason why panspermia has a following.

Re. the mathematical basis of natural events, including speciation: one or two contributors completely missed it. I have pointed this out on previous pages. There is a complete difference between the nature of the work of the Commonwealth Statistician and the men who built the Sydney Harbour Bridge. You don’t transform one species into another by cataloguing details: you DO it. Refer to Kelvin’s “Stamp Collecting” quote. In science there is Physics; everything else is stamp collecting. One can collect and statistically analyze stamps ad infinitum; it need not increase one’s knowledge of how paper is manufactured. The explanation of the mechanism of speciation as presented on this page is of the same category as ideas that were held before microscopes -e.g., dust gives rise to fleas. “Divergence within a population gives rise to new species”. Hey, presto. It does it because it does it. For fine details, consult my world view? To assist the one or two contributors who apparently have poor English cognitive skills - fighting trash science with trash science is having the effect of making the other side (e.g, AIG)look better. What the heck does all this matter, anyway?

Philip Heywood Wrote:

I am enlightened re. chaos - o.k.. Chaos theory as you describe it certainly must have applications in nature.

Indeed it does.

The idea that biological systems are chaotic in the sense of being ultimately unguided is manifestly difficult.

I’m not sure what “manifestly difficult” means, but that idea is certainly outside the purview of science. Evolutionary theory isn’t concerned with whether evolution is “ultimately guided” or not. It clearly is partially guided in a non-volitional sense by natural selection. You are welcome to speculate about whether or not that guidance and the apparently random contributions of mutation and genetic drift represent an ineffable divine plan or not, but that’s not science.

Do the probability on things being like they are, beginning with “primordial soup”, or the “big bang”, or whatever one chooses.

No, please, don’t do it. There is no meaningful “probability on things being like they are” from an arbitrarily distant beginning. Probability calculations, like any calculations, require assumptions and input values. There’s no way to compute the probability of everything.

Start with a mixture of chemicals: end with a microbe. Already the probability requirements have blown out to be approaching infinity.

No. The probability is, plain and simple, unknown and unknowable. No one has ever properly computed it and, until we have computers capable of simulating entire solar systems down to the subatomic level for billions of years, no one ever will.

And please don’t say “We don’t know it exactly, but we know it’s really small.” We don’t know that at all. Every probabilistic attempt to prove that relies on invalid mathematics, such as assuming that all the chemical reactions consist of random chemicals thrown at each other at high speed in a vacuum.

Refer to Kelvin’s “Stamp Collecting” quote. In science there is Physics; everything else is stamp collecting.

Kelvin, unfortunately, got utterly owned by the biologists and geologists, whose “stamp collecting” turned out to provide much better indicators of the age of the Earth than did his thermodynamic calculations. Beautiful hypotheses are slain by ugly facts, as Huxley said, and it’s the stamp collectors who find the facts.

As a stamp collector, I would entreat you, Dear Heywood, to read Candide. You will find the root of your probability nonsense slain and bleeding.

What the heck does all this matter, anyway?

if you can’t see the value of this kind of research, why are you even bothering to comment on it?

stamp collecting.…

Isn’t that one of Dave Scot Springerbot’s favorite arguments?

I think you should spend less time on UD and AIG, there, Phillip.

Thinking you will learn anything of relelvance on either site really is like watching “Marcus Welby, MD” on TV and thinking it has anything to do with actual medicine.

Posted by KiwiInOz on May 31, 2006 09:49 PM (e)

If anyone out there is a rain god then we could sure do with you visiting us here in Australia!

You can borrow ours, KIO. David “Fox Mulder” Duchovny was right. My part of the world is like a tropical rainforest… without the tropics. Ginormous blackberries, though, mmmmmm…

I have this annoying taskmaster that abhors technical anomalies. Forgive the pedantry. I spend no time with AIG. They wouldn’t have me. Who/what is UD? The enchanting Candide? Don’t feel obliged. I have to go and try to make a dollar.

For the record - personally, I would much prefer it if the people who claim to be the lights of knowledge & learning would focus better - Lord Kelvin was not an opponent of an old earth on principle - he could be said to have leaned towards panspermia, but in a purely speculative sense; yes, he couldn’t adjust to the nuclear age which was then dawning and so persisted with a soon-to-be obsolete model of the sun - hence his problems with an earth that wasn’t as old as it should have been. He was presumably older than he should have been when he retired. His physical chemistry stands for all time unchallenged, and is part of the basis upon which men such as Einstein and Planck built. In other words, select from other men’s works those things which are bound to be reliable, don’t make dogmatic statements unless you are certain of your ground, retire at a proper time, and live in expectation that tomorrow’s technology will solve today’s controversy. It has. Wish it would earn me a dollar. Best wishes.

fnxtr:

My part of the world is like a tropical rainforest… without the tropics. Ginormous blackberries, though, mmmmmm…

Pacific Northwest? Or possibly a container of fruit yogurt, in which all the vowels have already been consumed?

I spend no time with AIG. They wouldn’t have me.

Too nutty even for the nutters, huh.

Perhaps you should lay off the pot for a while, dude. It’s frying what’s left of your brain.

(sigh)

Philip Heywood Wrote:

don’t make dogmatic statements unless you are certain of your ground

That’s an excellent philosophy.

“Mathematics is definitely not my strong point, but I have an impression Einstein struggled with this concept of randomness (is that chaos?) and Hawkings reckons he’s got the physical universe fairly well in the bag, maths - wise, except for gravity. I suspect we might find that maths-physicists have a somewhat more rigorous definition of nature/the physical than do some of us in the descriptive professions.”

The short, sweet and professional answer has Anton given. Looking at the posts I think this is what is needed here. Just a few comments anyway for my amusement:

- Theory isn’t all math. Sometimes it is hard to realise theory with math or conversely build general theory on established particular math models.

- Physicists doesn’t think they can explain all the universe. And chemistry and biology emerges alongside, each better explained in their own terms.

- More forceful formal theories, like much of math, may be forever extended as a consequence of Gödels first incompleteness theorem. Which is nice since science never ends and since its formal structures are up to the task of modelling nature. OTOH, since they are up to the task it seems also nature is forever in need of more theory. Nature and theory may come arbitrarily close, but they aren’t exactly the same thing.

- Chaos is mainly a property of classical systems. Classical systems may have chaos since they may have exponential divergencies. Quantum systems doesn’t have fundamental chaos since they have linear divergencies instead. (In the semiclassical regime they may display it.)

- Randomness is another property. In classical system you see randomness as a property of coarsegrained systems. But in quantum system randomness is fundamental and finegrained.

steviepinhead:

Pacific Northwest?

Yes. Vancouver Island.

Or possibly a container of fruit yogurt, in which all the vowels have already been consumed?

Huh?

Is it pronounced Stevie pi-NADE? As in Brian?

Don’t know about the pie-nade guy, but I do know about Vancouver Island, living in Seattle as I do (and having lived in B.C. for a coupla years back in the fabled ’80s). Spent an excellent several days beach camping in the Pacific Rim National Park summer before last, north of Ucluelet and soutn of Tofino.

(Forget about the yogurt thing–just a lamely non-humorous effort to imagine another very damp place with blackberries! And the lack of vowels thing referred only to your “screen name.”)

Steviepinhead:

Brian Pinhead is one of two television newscasters on The Tick. He pronounces his last name pin-AID.

As for the screen name, vowel-free writing is a time-honoured tradition.

Right, Carole?

And yes, Long Beach is gorgeous.

About this Entry

This page contains a single entry by Mike Dunford published on May 30, 2006 8:06 PM.

How many species 2: What is a species, and Why does it matter? was the previous entry in this blog.

Intelligent Design Lacks Fertility is the next entry in this blog.

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