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Alrighty, I have a reasonable level of experience as a phylogeneticst and systematist. In contemporary systematics, the word race is generally used to describe different karyotypes within the same species. As humans are generally all 2n=46, the use of the word race to describe phenotypically or genetically distinct groups of humans is somewhat antiquated. Subspecies is a bit of a squishy topic, insofar as it is more a categorization of convenience than one with objectively defined characteristics. Generally, it defines a group with some diagnostic molecular or phenotypic characters, or groups with allopatric distributions, but some degree of admixture between them. One could pose an argument that different populations of humans are "subspecies", but there are a number of reasons why not: 1) Humans are a very, very recent group with very limited genetic diversity. 2) Genetic differences between human populations are generally clinal (with some exceptions of course). 3) Phenotypic traits are generally not fixed between groups of humans, and exist in a plethora of intermediate states. 4) The argument is all too often underlain by some sort of racist pseudoscientific motivation. While there is certainly valid population structure within Homo sapiens, and one could make an argument to taxonomically split the species into subspecies, I would imagine that such a designation would be of limited practical utility, fraught with ethical dilemmas and unlikely to be widely adopted. Edit to add: People publishing novel taxonomic arrangements that no one else agrees with happens all the time. If it's bad enough, scientists in the field will simply ignore the erroneous classification, then get super annoyed that when you do revise the group properly, the International Commission of Zoological Nomenclature code dictates you have to use the existing names the crackpot registered.

Matter and galaxies do not expand, their binding energy is far stronger than the energy supplied by the cosmological constant. So no this is inaccurate to describe why the universe expands. lets try a little lesson. Pick any number of arbitrary points, as expansion occurs those points gain separation distance. However and this is the critical part, the angles between any two or more points do not change. This describes a homogeneous and isotropic expansion. So there is no flow of matter from some centre to the outer regions. Expansion occurs in all directions equally. If you think about this then consider the directional direction component of how forces work, then one also has to realize that no force style effect can be causing expansion. Take an object such as a star, or galaxy. Apply equal amounts of force on every side and angle from other objects gravity etc. That star or galaxy will not move as the net sum of forces at any given angle is zero. This is because the mass density distribution on all sides of the star or galaxy is equal so any force they may exert is also equal on all angles. In regions where there is zero to minimal binding energy expansion occurs as the extremely low energy density of the cosmological constant term roughly [latex] 7.0*10^{-10} joules/m^3 [/latex] has no binding forces to contend with, however neither does it have a directional component. It is only in regions where there is minimal matter/mass that expansion occurs (without any inherent direction). Now keep the above in mind for any speculation you may have. make sure your speculation can match the above criteria and furthermore match the criteria of no net inflow or outflow of mass/energy leaving or entering the cosmological event horizon. (limit of our Observable universe) simply we cannot get signals beyond this point as it takes time for signals to reach us. Both due to the speed of light as well as expansion rates. These criteria will greatly limit the options that one can speculate on that will fit the observational data. A great deal of professional models were discounted simply due to the extreme uniformity and homogeneous and isotropic distribution of matter. The second criteria can be tested by temperature measurements, so models such as Universe in a black hole/white hole has great difficulty meeting the first two criteria. With the uniformity and non directional component of expansion, the process causing expansion must occur everywhere equally. It can be overpowered in localized regions of matter and still occur (that region will simply not expand as a result). This is the conditions you must match to have validity. The process cannot be from localized sources such as galaxies etc as it takes time for signals to reach other locations limited by the constant c. For this reason must occur at al locations in some process. (simply overpowered by other binding energies in those localized mass densities). There is nothing wrong with speculations, however its a real time saver to know the criteria that one needs to meet and match in observational data.

I have no idea what you are talking about.

Originally, there are two major divisions of science - Natural sciences and Social sciences; Natural sciences are disciplines designed to predict and explain events that occur in our natural environment (Physics, Biology, Chemistry...), while Social sciences are usually fields of academic scholarship which explore aspects of human society (law, history, sociology...). From this, it is clear enough to state that natural sciences study the psychical world, and social sciences study human behavior. This being said, we can easily decide in which category does Linguistics fall; Linguistics is known as the scientific study of language and its form, meaning and structure, including the study of grammar, syntax and phonetics. However, Linguistics is a rather vast field of study and it can be divided in specific branches, such as psycholinguistics, sociolinguistics, computational linguistics, etc. According to this official and standard definition, Linguistics seems to fall under the category of Social sciences - since it studies a certain aspect of human behavior. However, linguistics tends to have different aspects of which some of those aspects belong to natural sciences, while others belong to social sciences. For instance, the aspects of linguistics that are related to natural sciences are neurolinguistics or biolinguistics. I think that this mix does not make linguistics and entirely social science, nor an entirely natural science, making it an interdisciplinary subject. But the fact that linguistics not being an entirely social science is not the problem here. The problem is the attitude that people have towards the two main divisions of science; Namely, the majority of people don't really value social sciences as much as natural sciences. And since most people put linguistics under the category of social sciences, they tend to automatically doubts its scientific credibility. But, i don't completely blame them, as they might have a good reason for their opinion. Another important argument as to why some sciences or disciplines of study may not be considered as "real sciences", and that has nothing to do with the fact that one particular science is considered as social or natural; A scientific study must have a valid approach and methodology, based on strong evidence, and not some claims or theories that cannot be subjected to an observational state. And only when these standards are met and achieved, the field of study that is in question can be considered as a real science that has some sort of validity in the overall scientific community.

So you assume that Jack knows that the range is 3. How does Jack think about the possibility that James knows that the product \(a\cdot b\cdot c \cdot d\) is equal to \(250\)?

Not really. But if you oppose the feeding of people who can't afford food, treating the sick that can't afford health insurance and protecting people who can't protect themselves then, yes - it makes them pretty despicable. Look up who Time magazine voted 'Man of the Year' in 1938. He was clearly more popular than you think... and so were his policies clearly as they are being copied today... but how far will YOU go with them? Not as far as he did I pray.

Perhaps you can do a better job answering questions, I for one see no reason you have presented not to use the following tables for fundamental constants including G https://arxiv.org/pdf/1507.07956.pdf

It is quite common in enumerative combinatorics to apply this kind of series expansion in situations where you want to count the number of different possible objects of some kind. In your example, the series \(A(x) = \sum_{n=0}^\infty x^n = 1 + 1\cdot x + 1\cdot x^2 + \cdots = \frac{1}{1-x}\) would give the answer to the "problem" ''How many natural numbers are there of size \(n\)?'' You get the answer by looking at the coefficient of \(x^n.\) In this application it makes no sense to "evaluate" a series at some value of \(x.\) The radius of convergence of the series does not play any role. In fact you may consider a series which counts the number of permutations \(n!\) of the numbers \(\{1,2,\ldots,n\}\): \[ P(x) = 0! + 1!\cdot x + 2!\cdot x^2 + \cdots = \sum_{n=0}^\infty n!x^n.\] Which has no convenient shorthand similar to \(A(x) = 1/(1-x)\) for the series \(A(x).\) In fact \(P(x)\) has zero radius of convergence; there is no value \(x \neq 0\) for which \(P(x)\) converges. And yet the series makes complete sense combinatorially.

Hi Michel, I do not see your problem. Everytime when one extends the set of numbers you get surprises: N: 1,2,3,4,... When multiplying 2 natural numbers the result is always >= both numbers. Z: ... -2,-1,0,1,2... Ups, the above rule is not valid anymore: -2 * 4 = -8: the result is smaller than both numbers! Same if you use Q+: 0.1 * 0.2 = 0.02: again, the result is smaller than both numbers. Now with imaginary numbers you get the next surprise: where in the above sets at least the square of a number is always positive, this is not so with imaginary numbers. (i)2 = -1, as is (-i)2. So rules that seem general (plus times plus makes plus, minus times minus makes also plus) for a subset of all numbers (Z, Q, R), is not valid for C anymore. And as Studiot also explained, the principle of ordering (greater, smaller) in C does not work. The question if i is greater than 1 does not make sense. Therefore C is depicted in a two dimensional plane.

You assume people are not reading or understanding because they disagree with you. The problem is that you are wrong and refuse to admit it. I have provided references to research that shows it is not a meaningful or useful concept. You have provided your assertions and beliefs. At least one definition of race is based on genetics. Another assertion without evidence. Yes, all you do is repeat yourself. I will report this thread for soapboxing as you are unable to engage in discussion. For Christs sake! Don't make me repeat myself every hour! Instead please reread my posts every hour. That would be less work on my part. This is getting ridiculous. It's like you guys know my opinion better than I do. As I was saying before it's like you have preconceived ideas of anyone that talks about race. You have your canned replies that don't pertain to my remarks. It was you that said race is based on superficial appearances. So I picked a superficial appearance which must, by your definition, define a race. Instead of getting annoyed that people are pointing out the inconsistencies and errors in your claims, maybe you should stop making baseless claims. So who gets to choose which superficial differences are significant and which are not? Not really. Over time populations that have migrated often tend to look like the "native" inhabitants. For example, gypsies (in Europe) look European. It is pretty much only their language that show they originated in India. The evidence still shows you are wrong.

..download Visual Studio Express, and write some C/C++/C# app..

Do you know what 'arbitrary' means?

I was too once but then it hit me.

'Cock'', 'Knob' and 'Dick' are used here in the same way, and they refer to male genitals, so it's all fair and square gender-wise.

I'm so sincerely glad you got a better job , since this cite obviously is not your vocation , and the presentation surely is either way boring .But thank you for "reading" the numbers.

I refuse to respond to any of your posts until you reread this thread. Be careful to understand my posts before you reply. Please start with my very first post. I am tired of repeatedly posting the same thing over and and over again just to have people accuse me of saying things I have never said. You see the title says someone is asking if there "are different human races". From that you have a preconceived notion of what I have to say. Anyone that thinks human races are different is a racist. Racists think they know the races. Racists will overgeneralize with few statistics. They will find stats that support their view instead of developing their view to support to support facts they are collected without bias. A racist may first decide that a certain race is more prone to break laws. Then he'll go out and find specific examples of people of that race getting arrested and say that substantiates his claim that the race is prone to crime. This is what you are doing to me. You have preconceived notions of what my intentions are and you don't listen to the ideas of me as an individual. Almost none of your rebuttals pertain to my beliefs that I have made clear. You search our stats that fit your preconceived notion of what you think I believe. Strange, you are only a little better. But once again, all of science does not say race is a meaningless concept. Broader sciences such as biology don't like the word "race" because it can't be outlined definitively with genetics. More specific sciences such as ornithology very much like the term race because it can tell where a specific bird originally came from. The same can be said of humans. Once again I find myself repeating myself again and again and again and again and again, just to have someone put words into my mouth that have nothing to do with my stand on the topic. For Christs sake! Don't make me repeat myself every hour! Instead please reread my posts every hour. That would be less work on my part. This is getting ridiculous. It's like you guys know my opinion better than I do. As I was saying before it's like you have preconceived ideas of anyone that talks about race. You have your canned replies that don't pertain to my remarks.