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We didn’t know randomness could be “subtle”

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  From Peter Woit at Not Even Wrong:

Erica Klarreich at Quanta has the story of a surprising new result about prime numbers from Kannan Soundararajan and Rober Lemke Oliver. They have found that, given a prime number with a certain last digit, there are different probability for the last digit of the next one (among the various possibilities). This violates usual assumptions that such things are in some sense “random”, indicating just how subtle this “randomness” is. More.

From Klarreich at Quanta:

Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers — those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them.

Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9. In a paper posted online today, Kannan Soundararajan and Robert Lemke Oliver of Stanford University present both numerical and theoretical evidence that prime numbers repel other would-be primes that end in the same digit, and have varied predilections for being followed by primes ending in the other possible final digits.

The discovery is the exact opposite of what most mathematicians would have predicted, said Ken Ono, a number theorist at Emory University in Atlanta. …

See also: Infinity at Starbucks: Starring Laszlo Bencze and Art Battson

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Comments
Mapou #99
All the Darwinists, atheists and materialists who comment on UD are church missionaries who come here to proselytize for the Church of the Flying Dirt Monster. They are here to try to convert Christians to their stupid dirt worshipping religion.
Your own views, disputed by many physicists, could be characterised as strictly beliefs and not facts. Should your views be subject to similar censorship?
In my opinion, UD should prohibit all proselytizing behavior by the atheists. They should go to their own internet sites and talk among themselves. They continually treat Christians like dirt on their own websites and discussion forums but when they come here, they expect to be treated with dignity.
I am hardly ever treated with dignity on UD by the likes of you. But the site rules say I should be. And you are in blatant violation of those rules. And the site moderators tolerate your behaviour. Which means they have double standards.
I personally refuse to treat them with nothing but contempt and total disrespect. If the UD moderators decide to ban me for this reason, then so be it. My only request is this: Do not let the dirt worshippers come here and shed their crocodile tears like a bunch of hypocritical crybabies and demand to be treated fairly. Do not let them dictate anything on UD. They deserve to be vilified and worse.
If the site moderators agree with you then they should be clear and change their moderation policies. Agreed?ellazimm
March 26, 2016
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By the way, does anybody on UD know of a good artist/cartoonist who can draw some kind of Flying Dirt Monster? I would love to see a few good representative renditions or interpretations of the concept.Mapou
March 26, 2016
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If you don’t care, why did you respond?
And pass up a chance to disrespect a dirt worshipper? No way. Just get back to your Flying Dirt Monster church and leave us alone.Mapou
March 26, 2016
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"Man, go pack sand up your asteroid and see if I care." If you don't care, why did you respond?Indiana Effigy
March 26, 2016
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All the Darwinists, atheists and materialists who comment on UD are church missionaries who come here to proselytize for the Church of the Flying Dirt Monster. They are here to try to convert Christians to their stupid dirt worshipping religion. In my opinion, UD should prohibit all proselytizing behavior by the atheists. They should go to their own internet sites and talk among themselves. They continually treat Christians like dirt on their own websites and discussion forums but when they come here, they expect to be treated with dignity. I personally refuse to treat them with nothing but contempt and total disrespect. If the UD moderators decide to ban me for this reason, then so be it. My only request is this: Do not let the dirt worshippers come here and shed their crocodile tears like a bunch of hypocritical crybabies and demand to be treated fairly. Do not let them dictate anything on UD. They deserve to be vilified and worse. Just my opinion.Mapou
March 26, 2016
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Indiana Effigy, Man, go pack sand up your asteroid and see if I care. Crybabies.Mapou
March 26, 2016
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Mapou: " I speak what’s on my mind, .." Given your limited vocabulary and ideas, this is painfully obvious. "The combinatorial explosion just crushed your little chicken feather voodoo religion." This pet concept of yours (one of your two catchphrases) was soundly destroyed over on Dr. Hunter's blog. Your intelligent and well thought out response was your second response. As the moderators here apparently have no desire to prevent your abusive comments, this will be my last response to one of your comments until you have something informative to say.Indiana Effigy
March 26, 2016
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UD moderators I would like to know why Mapou is allowed to refer to other commentators as he does in #89
You people are not just a dirt worshippers, you are a bunch of lying, door-to-door missionaries with stupid beady eyes, selling holy dirt.
If I used such language you would bounce me out lickity-split.
I’m sure you would love to shut me off but I am indeed special, compared to a bunch of small-cranium, cargo-cult primitives in need of remedial math. I speak what’s on my mind, whether or not I am banned by UD moderators. If you don’t like it, go pack sand somewhere and see if I care. LOL
Can you honestly say Mapou is following your guidelines for participation in UD? And from #91
The search space increases exponentially with every new variable. The combinatorial explosion just crushed your little chicken feather voodoo religion. Go back to school and learn some simple math, you tree-dwelling primitive.
Is this really the sort of style you wish to uphold here?ellazimm
March 26, 2016
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Origenes #87
If so, then despite the cull. To state the obvious: the elimination of certain (less fit) body plans reduces the total amount of body plans.
Except the culling I'm talking about is just that that occurs in every generation which means we're not talking major differences in body plans. AND, it's still true that the generation generated by those who were 'selected' has more genetic variation than their 'parents'. Each generation has new variations.
Nope. New body plans are entirely produced by randomness. The cull is not a creative part of the evolutionary process. Organisms that continue to live can be said to escape the cull — they are “untouched” by the cull.
The cull decides which variations to keep and the new variation is on top of that. The cull helps 'direct' evolution. Each generation differs only in very, very small ways from the previous generation if at all.
If so, then despite the cull.
You're not understanding me I think. Generation1 is culled down to a subset which generate offspring. Call them Parents1. Generation2 comes from Parents1 and Generation2 has more genetic variation than Parents1. Has to. Because of mutations during breeding.
I never disputed this adaption effect of the cull. However, give it some thought and you will understand that nothing creative is going on.
'Creative' is a somewhat laden word. I say new body plans come from generation upon generation of cumulative selection acting on random variation.ellazimm
March 26, 2016
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Origenes: Because resources are limited we see a general increase in size? If every organisms that could ever be born remained in the population, then we would see the distribution of traits spread out. We would see every possible organism, including a vast majority of those which would not be able to survive in the real world (such as a billions of species of large blobs without circulatory systems or lungs or even means to ingest food). In this imaginary world, there would be no limit on space or resources, so the mass of living tissue would exceed that of the Sun in a few thousand years, and the mass of the galaxy in a few thousand years more. But in the real world there are limits. What we see are examples of positive selection, such that if we were to look over a period of time, we often see traits moving with a specific tendency, such as skull size in the genus Homo.Zachriel
March 26, 2016
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It seems to me that Mapou is deliberately testing the limits of how far he can go in insulting people. One of my favorite Calvin and Hobbes cartoons is when Calvin asks his dad how they know that a bridge has a 6 ton limit. His dad says, "They keep driving bigger and bigger trucks over it until it breaks. Then they know what the limit is, and then they rebuild the bridge." Mapou is possibly applying this method. He says he doesn't care if he's banned, so he has no reason to restrain himself, it seems.Aleta
March 25, 2016
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Zachriel: However, because resources are limited, and depending on the environment, what we might see is an general increase in size over time.
Because resources are limited we see a general increase in size? That doesn't make much sense to me, but even so, what is your point?Origenes
March 25, 2016
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Zachriel, the dirt worshipping psycho:
To take a simple example, given fecundity and unlimited resources, then we would expect an organism to grow taller and shorter and everything in between.
The search space increases exponentially with every new variable. The combinatorial explosion just crushed your little chicken feather voodoo religion. Go back to school and learn some simple math, you tree-dwelling primitive.Mapou
March 25, 2016
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Origenes: To state the obvious: the elimination of certain (less fit) body plans reduces the total amount of body plans. To take a simple example, given fecundity and unlimited resources, then we would expect an organism to grow taller and shorter and everything in between. However, because resources are limited, and depending on the environment, what we might see is an general increase in size over time. In other words, the actually history showing a definite tendency.Zachriel
March 25, 2016
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ellazimm, the dirt worshipper:
Except that no is saying life arouse from dirt.
You people are not just a dirt worshippers, you are a bunch of lying, door-to-door missionaries with stupid beady eyes, selling holy dirt.
I know you’ve made up your mind and arguing with you is a waste of time but I can’t understand how the moderators of this site continue to let you get away with abusive language and behaviour. I guess you’re special.
I'm sure you would love to shut me off but I am indeed special, compared to a bunch of small-cranium, cargo-cult primitives in need of remedial math. I speak what's on my mind, whether or not I am banned by UD moderators. If you don't like it, go pack sand somewhere and see if I care. LOLMapou
March 25, 2016
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KairosFocus, I don't want to derail this thread with off-topic discussions about history and the US constitution, but if you are willing to draft a short soap, I would gladly discuss it with you there.Indiana Effigy
March 25, 2016
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ellazimm : The repeated process of random generated variation, cull, repeat generates new body plans.
If so, then despite the cull. To state the obvious: the elimination of certain (less fit) body plans reduces the total amount of body plans.
ellazimm : It’s the effect of cumulative selection.
Nope. New body plans are entirely produced by randomness. The cull is not a creative part of the evolutionary process. Organisms that continue to live can be said to escape the cull — they are “untouched” by the cull. Colin Patterson describes natural selection as a 'weeding out process' that leaves the stronger progeny. “The stronger progeny must be already there; it is not produced by natural selection...selection is made from already existing entities.”
ellazimm : Every new generation has more genetic diversity than its parents, those ‘selected’ from the previous generation.
If so, then despite the cull.
ellazimm : You focus on the effect of a single cull. Consider the effect of cumulative selection over generations and generations of cumulative variation. Those that ‘make it’ are better adapted to their environment.
I never disputed this adaption effect of the cull. However, give it some thought and you will understand that nothing creative is going on.Origenes
March 25, 2016
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IE, au contraire, one of the lessons of sound history is that it teaches us alternatives and possibilities constituting lessons bought in blood and tears that we had better heed or else; those who would reduce history to victory propaganda or dismiss it as inevitably such or even deride it as meaningless bunk, have a terrible responsibility. The latin american and european experiences across C16 - 20 show us very relevant examples on what disunity on a continental scale easily leads to, as arguably happened with the American Civil War also -- just the opposite of what you tried to claim. Perhaps, you did not notice that in parallel to the 1830's the British Empire went through a slavery and slave trade debate and policy process that led to peaceful abolition 1834 - 38. It is not merely the compromise that led to civil war in the US. It is regional polarisation that refused to seriously work through the legacy of the founders on the significance of the image of God and consequent right to liberty. As a deposit of creation. Where, every mixed race child or descendant stood and stands in proof that we are of one blood -- a standing rebuke to racism. KF PS: Actually, it is clear that a material input to how Britain handled other territories was the lesson of the American Revolution. And had the British elites taken Magna Carta and the 1689 Bill of Rights to heart, there would have been no revolution. In our day, I think we have a few lessons to learn from Alfred the Great of Wessex's Book of Dooms.kairosfocus
March 25, 2016
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Indiana Effigy: I think, therefore I am. Feel free to quote me on this.
Given materialism there is no "I" who thinks. Instead thoughts are being produced entirely by unthinking non-rational brain chemicals. The existence of a free responsible rational agent "I" cannot be grounded in a universe containing nothing over and beyond the physical.Origenes
March 25, 2016
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KairosFocus: "Do tell us, what would have been the predictable result of failure to fix the major governance problems of the fledgling American republic in the 1780’s, at whatever price of compromises?" You can't predict what would have happened. That is a fools game. But you can definitely say what did happen. The compromise resulted in a war that killed more Anericans than all other wars combined and produced a black/ site rift that probably won't get better any time soon. But, since you insist on playing the what would have happened game, I will play along. What would have happened if there was no revolution? We can't say for certain but we can look at a few countries that opted for this approach. Canada, Australia and New Zealand. No civil war. Racial issues but nowhere near as institutionalized as in the US.Indiana Effigy
March 25, 2016
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EZ, Yes, the US Const came at the early stages of the struggle and compromises were forced at a time when overall abolition was not typically seen as possible. Equiano for one (a former slave who obtained freedom here in M/rat in the 1760s it seems), participated in an attempt to ameliorate in IIRC Nicaragua. Law always addresses realities of the time including balances of power. In that context the Const set a sunset on the trade, the root of the problem and its most vulnerable point on grounds of kidnapping. Which Equiano exemplified. As noted the 3/5 provision implies personhood of slaves and crucially blocked domination of the legislature, which affected the onward balance. Do tell us, what would have been the predictable result of failure to fix the major governance problems of the fledgling American republic in the 1780's, at whatever price of compromises? Would a world of breakdowns and division open to external interference and rise of local dominant oligarchies as in Latin America have been a better outcome? Do you or others really want to argue that claim, given the history of Latin America? KF PS: For reference Wiki on the C19 history of Latin America:
The failed efforts in Spanish America to keep together most of the initial large states that emerged from independence— Gran Colombia, the Federal Republic of Central America[13] and the United Provinces of South America—resulted a number of domestic and interstate conflicts, which plagued the new countries. Brazil, in contrast to its Hispanic neighbors, remained a united monarchy and avoided the problem of civil and interstate wars. Domestic wars were often fights between federalists and centrists who ended up asserted themselves through the military repression of their opponents at the expense of civilian political life. The new nations inherited the cultural diversity of the colonial era and strived to create a new identity based around the shared European (Spanish or Portuguese) language and culture. Within each country, however, there were cultural and class divisions that created tension and hurt national unity. For the next few decades there was a long process to create a sense of nationality. Most of the new national borders were created around the often centuries-old audiencia jurisdictions or the Bourbon intendancies, which had become areas of political identity. In many areas the borders were unstable, since the new states fought wars with each other to gain access to resources, especially in the second half of the nineteenth century. The more important conflicts were the Paraguayan War (1864–70; also known as the War of the Triple Alliance) and the War of the Pacific (1879–84). The Paraguayan War pitted Argentina, Brazil and Uruguay against Paraguay, which was utterly defeated. As a result, Paraguay suffered a demographic collapse: the population went from an estimated 525,000 persons in 1864 to 221,000 in 1871 and out of this last population, only around 28,000 were men. In the War of the Pacific, Chile defeated the combined forces of Bolivia and Peru. Chile gained control of saltpeter-rich areas, previously controlled by Peru and Bolivia, and Bolivia became a land-locked nation. By mid-century the region also confronted a growing United States, seeking to expand on the North American continent and extend its influence in the hemisphere. In Mexican–American War (1846–48), Mexico lost over half of its territory to the United States. In the 1860s France attempted to indirectly control Mexico. In South America, Brazil consolidated its control of large swaths of the Amazon Basin at the expense of its neighbors. In the 1880s the United States implemented an aggressive policy to defend and expand its political and economic interests in all of Latin America, which culminated in the creation of the Pan-American Conference, the successful completion of the Panama Canal and the United States intervention in the final Cuban war of independence.
kairosfocus
March 25, 2016
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EZ, so many strawmen, so little time. It is you who need to account for the first common ancestral organism on blind chance and mechanical necessity in Darwin's pond or the like, then its diversification into major body plans, duly backed by actual empirical demonstration of the capacity of sid mechanisms. No one, least me, talks of turning a cockroach or even a roach swimming in the Thames, into a beluga or a blue whale. The issue is, justify the claim of the tree of life on teh mechanism proposed. The distractions are demonstration enough that the problem has not been cogently addressed. Islands of function, as I and others such as GP have noted repeatedly, start at molecular levels. The change in organisms, the presence of singletons and small fold domains isolated structurally from even morphologically close species and the need for 10 - 100+ mn base pairs of fresh info to form a new body plan are neough challenge. Unanswered. The only empirically warranted causal factor sufficient to explain FSCO/I is design, right from the root of the tree on up. And it is not rough landscapes that are my concern, but the flooding by a sea of non-function that deeply isolates islands and archipelagos of function, such that getting across the seas to shorelines of function dominates any convenient discussion on hill climbing or its kissing cousins. Again, predictably, not adequately addressed. KF PS: On self evident, foundaitonal truths, start with A say a bright red ball on a table, and ponder the world partition imposed by the distinct identity: W = {A |~A} I suggest that A is A, that A cannot at once be not A, and that something x will be A, or else not A, and not both or neither, are self evident, unassailable truths prior to any further reasoning and communication, not subject to subjectivist or relativist whims and fashions of thought. In that context, something like, error exists, will be found to be undeniably true on pain of self refuting absurdity. And so forth, in short the symptom of relativism is pointing to deep roots of the mess we see all around.kairosfocus
March 25, 2016
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Mapou #80
All Darwinists are dirt worshipping morons. LOL
Except that no is saying life arouse from dirt. I know you've made up your mind and arguing with you is a waste of time but I can't understand how the moderators of this site continue to let you get away with abusive language and behaviour. I guess you're special.ellazimm
March 25, 2016
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All Darwinists are dirt worshipping morons. LOLMapou
March 24, 2016
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Mapoo: "That’s an answer that only a jackass would give. What is wrong with you?" Yes, it does sound like something that you would say.Indiana Effigy
March 24, 2016
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Effigy, are backtracking on what you wrote earlier? I was talking about how the Constitution forbids the teaching of religion in our public schools and how Darwinists, atheists and materialists believe and teach our children in our taxpayer-funded schools to believe that life arose from dirt and that single cell organisms changed themselves into crocodiles, whales and humans. I maintain that this is a chicken sh!t religion and should not be taught in public schools because it violates our constitutional rights. Those who do so should be prosecuted and jailed according to the law. You replied:
Sorry Mapou, but I could care less about your constitution. It also embraces slavery. Not something to be proud of.
That's an answer that only a jackass would give. What is wrong with you?Mapou
March 24, 2016
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Axel #75
Mathematics falls within the definition of a priori truth. So you do get the primacy of a priori truths?
Mathematical truths/theorems are true because they can be proved. What was true in mathematics 2000 years ago is still true.
If you think truth is a slippery notion and don’t believe in absolute truth, just ‘personal’ truths, and you want to convince others of the characteristically atheist rationality of that perspective on everything, you are really just trying to promote nihilism, and even by your own criteria, heeding your opinion or anyone else’s is senseless.
I don't believe in 'personal' truths. I believe in those things that have been established independent of any one person's say so. Nothing to do with theology, that's your bias view of my belief structure. Nothing to do with nihilism either; you consider my view dry and dusty but that's just your opinion. My personal views are as meaningful and as meaningless as anyone else's which is why I don't base my world view on them.ellazimm
March 24, 2016
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specter13 #74
You talk about physical things which can be examined as truth and then denigrate logic which can be misinterpreted or false – there is no value in whatever data you assess until ‘you’ through intentionality give it some. Numbers don’t exist in any physical sense, therefore neither do your measurements. In that case the moment you have a thought you have employed reason & logic, no matter how vacant and absurd it may be.
Something which can be measured can be examined over and over again by others to avoid misinterpretation. Units of measurements are agreed upon standards but a thing is what it is and does not change its size based on opinion or interpretation. The method of measurement may give different results though . . . interesting stuff.
Google Zeno’s dichotomy paradox
That's basic, undergraduate stuff. If you really want to get your teeth into something look at Cantor's work or even more recent work with surreal numbers. How about fractal dimensions in accordance with Mandelbrot's research. If you want to talk mathematics then you'd be advised to NOT use an ancient example of a paradox.ellazimm
March 24, 2016
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ellazim 71 : Mathematics falls within the definition of a priori truth. So you do get the primacy of a priori truths? If you think truth is a slippery notion and don't believe in absolute truth, just 'personal' truths, and you want to convince others of the characteristically atheist rationality of that perspective on everything, you are really just trying to promote nihilism, and even by your own criteria, heeding your opinion or anyone else's is senseless.Axel
March 24, 2016
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EZ "In my experience what is and what is not considered a true logical assumption has shifted over the centuries. Since it’s easy to recall logical men who have advocated genocide I think I’ll stick with physical evidence. I agree it can be distorted and mis-interpreted but it is a physical things which can be examined and looked at." You talk about physical things which can be examined as truth and then denigrate logic which can be misinterpreted or false - there is no value in whatever data you assess until 'you' through intentionality give it some. Numbers don't exist in any physical sense, therefore neither do your measurements. In that case the moment you have a thought you have employed reason & logic, no matter how vacant and absurd it may be. EZ "We all have our own truths. Except for mathematics, I find them all provisional. Only mathematics has theorems." Google Zeno's dichotomy paradoxspecter13
March 24, 2016
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