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According to the bible Jesus Christ was a supernatural character who could walk on water, occasionally talked to Satan, and could turn water into wine, amongst many other marvels. Can you be a scientist and still believe in this stuff? As far as I am concerned, you should not be called a scientist or be allowed anywhere near any scientific endeavour if you believe in fictitious myths. Am I being too aggressive in my attitude? Probably, however science and the scientific approach to research application is a serious technical field that should not be sullied by ridiculous fairy tales. >Please move to the Religion section..

Question: I understand that close-in planets in a red-dwarf system are probably tidally locked. However, if the planet had a large moon, would the tidal locking be avoided? Would the tug of the moon keep the planet from being locked? Thanks.

There is and it starts with you and I, we can stop buying stuff we don't need (like plastic nik-nak's and unethical banking products) and minimise travel that we don't need or maximise human power (cycling, walking etc.), and maybe go veggie/vegan (a step to far for me); people who can afford to choose are responsible for change.

Who are we to say what should amaze us as individuals.... very narrow-minded views, I must say. .

That is a big topic and it all depends on which slaves are and time frame you are looking at. However, chattle slavery was, as the name implies, certainly not a voluntary emigration process (there are folks that try to frame it that way, but that is basically insane). Edit to add: I think the Spanish had some theoretical protections for the indigenous in place, including banishing their enslavement sometime in the 16th or so century. But instead they had "coerced labour" which basically was mandatory unpaid labor with dubious benefits like converting them to Christianity. I suspect that what you have in mind is the trans-Atlantic slave trade which roughly happened between ~ 16th and 19th century. Considering the huge time span the details of the trade have changed quite a bit as has the volume throughout the periods. Also, the how slaves were viewed. increasingly as commodity has changed somewhat over the centuries. Partially because initially slavery was not something associated with a specific population (but rather with bouts of misfortune, such as losing a conflict) and often routes of freedom were built into the system to some degree. That at some point vanished for the victims of the trans-Atlantic trade. One other thing to keep in mind is that Africa as a whole was not just an assembly of primitive tribe, as it is often present in the European imagination. Rather there were different kingdoms and empires present who had their own history of conflict. I.e. African history is not just one of white conquest, though especially in the years of colonization the influence of Europeans at some point became a dominant shaping force. Some of earliest reports involve maritime raiding, where a Portuguese Captain (Gonçalvez) kidnapped Berbers, and negotiated their freedom in exchanged for slaves. Around the same time, the church basically sanctioned slavery of "pagans". While the Portuguese conducted raids in West Africa, it was replaced mostly (I think) by a trade network involving African nobility. The slaves were baptized and transported to Portugal but were later also sold to Spain for their colonies There is a huge amount of literature in this area and my knowledge is basically non-existent. However, I think the first step is to acknowledge that the history of slavery is complex (as is basically everything) and that there are no simple narratives that would do the subject justice. One would need to dissect what is happening in a given time frame. As a kind of overarching narrative one could haphazardly argue that what initial started as "normal" European customs with regard to slavery (which tapered out by the mid 16th century) grew over time to a quite different system, driven by the demands of the new colonies and the profitability of the trade. But again, the details are quite complex and I am not sure whether they can be properly answered in a short post format (perhaps an expert could).

First you need to know that 0 and 1 are fractions themselves ! [math]0 = \frac{0}{1}\quad and\quad 1 = \frac{1}{1}[/math] Although we don't usually write them like that. Mathematics recognises a series of 'number systems' that are nested like Russian dolls. The outer one is the most complicated and the number systems get simpler inside just as the outer doll is the biggest and the dolls get smaller inside. For number systems the more complicated (outer) system contains or includes all the simpler systems within it. The simplest system is called the natural numbers or counting numbers. 1,2,3,4,5...... There is no zero in these. Then we have the positive inetgers if we want the same thing but with a zero 0,1,2,3,4,5...... The we have both positive and negative integers ...-5,-4,-3,-2,-1,0,1,2,3,4,5...... These are all the integers. The we have the rational numbers : ratios of two integers ie fractions [math]\frac{1}{2},\frac{{25}}{{39}}etc[/math] We do not need another category for the ratios of decimal numbers since they can always be written as the ratio of two integers [math]\frac{{2.5}}{{3.138}}is\;the\;same\;as\frac{{2500}}{{3138}}[/math] Which is a number system as far as you have asked since it includes all the fractions lying between 0 and 1 that can be written. And it also answers you question about number bases. Simply it does not matter which base you choose as shown by the example of rewriting a decimal fraction as the ratio of two integers. But there are yet more important numbers that cannot be written this way. An example would be the reciprocal of the square root of 2, or the square root of 0.5. So we come to the what are called the real numbers as corresponding to our outer Russian doll, and includes all these numbers as well as all the fractional ones. I hope you can see nesting idea from this. There are yet more complicated layers of 'numbers' but I will leave it at that.