We didn’t know randomness could be “subtle”

_{Denyse O'Leary

March 22, 2016

Mathematics, News}

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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: "Effigy is still spewing his crap on this thread? Did you not claim earlier that the US constitution embraces slavery? What kind of moron are you to think that you still have a say in anything on this blog after you spew out such vomit?" Then why was there a civil war over an amendment to abolish slavery? Why did the constitution require free states to return escaped slaves to their owners?Indiana Effigy_{March 24, 2016
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Slavery in the US Constitution From http://www.usconstitution.net/consttop_slav.html
Slavery is seen in the Constitution in a few key places. The first is in the Enumeration Clause, where representatives are apportioned. Each state is given a number of representatives based on its population - in that population, slaves, called "other persons," are counted as three-fifths of a whole person. This compromise was hard-fought, with Northerners wishing that slaves, legally property, be uncounted, much as mules and horses are uncounted. Southerners, however, well aware of the high proportion of slaves to the total population in their states, wanted them counted as whole persons despite their legal status. The three-fifths number was a ratio used by the Congress in contemporary legislation and was agreed upon with little debate. In Article 1, Section 9, Congress is limited, expressly, from prohibiting the "Importation" of slaves, before 1808. The slave trade was a bone of contention for many, with some who supported slavery abhorring the slave trade. The 1808 date, a compromise of 20 years, allowed the slave trade to continue, but placed a date-certain on its survival. Congress eventually passed a law outlawing the slave trade that became effective on January 1, 1808. The Fugitive Slave Clause is the last mention. In it, a problem that slave states had with extradition of escaped slaves was resolved. The laws of one state, the clause says, cannot excuse a person from "Service or Labour" in another state. The clause expressly requires that the state in which an escapee is found deliver the slave to the state he escaped from "on Claim of the Party."
I'm not saying the US Constitution 'embraces' slavery but it did not, initially, forbid it. That required an amendment.ellazimm_{March 24, 2016
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Axel #66
In very principle, it is a significant error to valorise empirical evidence over a priori truths and logical inferences. Physical evidence can become subject to atmospheric degradation, or be tampered with – as is often adduced concerning forensic evidence in trials and enquiries. A priori truths belong to another realm of unassailable integrity.
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.
If there is one thing any materialist ignores it’s logic. To a materialist logic is a crutch.
Logic is a tool. Very, very useful but subject to misuse like everything else.
Logic is always unassailable, partaking of the nature of a priori truth.
Truth is a slippery notion. Are protons 'true'? If they are really combinations of smaller particles does that makes them less true? Is free will 'true'? Does it actually exist or is it just a notion that we'd like to ascribe to ourselves so that we feel that we are independent agents? I know I'd like to believe that. But what does the data say? Is it 'true' that you love your partner? How can you prove that? We all have our own truths. Except for mathematics, I find them all provisional. Only mathematics has theorems.ellazimm_{March 24, 2016
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Effigy is still spewing his crap on this thread? Did you not claim earlier that the US constitution embraces slavery? What kind of moron are you to think that you still have a say in anything on this blog after you spew out such vomit?Mapou_{March 24, 2016
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I think, therefore I am. Feel free to quote me on this.Indiana Effigy_{March 24, 2016
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Their best comical effort of course is when the invoke reason to deny that reason exists....Andre_{March 24, 2016
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If there is one thing any materialist ignores it's logic. To a materialist logic is a crutch.Andre_{March 24, 2016
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ellazimm, your #64, Logic is always unassailable, partaking of the nature of a priori truth. It is the false premise that people can get so wrong, indeed, so wrong that, as Keynes remarked in a review he wrote of a book written by Hayek, they, end up 'in bedlam !' Led there of course by their impeccable logic applied to an erroneous premise. Point out any false premise in his argument in his post #62, or indeed, falsehood, i.e. illogical inference. In very principle, it is a significant error to valorise empirical evidence over a priori truths and logical inferences. Physical evidence can become subject to atmospheric degradation, or be tampered with - as is often adduced concerning forensic evidence in trials and enquiries. A priori truths belong to another realm of unassailable integrity.Axel_{March 24, 2016
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A lot of overloading in that statement; rationality, thinker, control, thoughts. Translation: That's asking me to think too much. Therefore it's false.Mung_{March 24, 2016
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Mike1962 #60
Hopefully gold bars are going to fly out of my arse someday. Wake me up when either happens.
Okey dokey. Axel #62
It totally undermines your materialism, exposing the ‘straw man’ constituting your response below. If he is clearly prejudiced, it can only be on the basis of the logic : in which case, it is a mandatory prejudice from the viewpoint of rational thought.
In the past 'logic' insisted the earth was the centre of the universe. Later 'logic' insisted the orbits of the planets had to be circles. I'll go with the data and experimental results. I'd rather not know than to draw a premature conclusion based on any human's ability to 'logic' the world. I never denied I was real as ba77 implies. I never called another human being a non-person as ba77 did. I'm open to new data and discoveries. I think we still have a lot to discover. I suspect there are lots of things we will probably never know. I don't prefer armchair proofs over observable results.ellazimm_{March 24, 2016
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bornagain77: (1) rationality implies a thinker in control of thoughts. A lot of overloading in that statement; rationality, thinker, control, thoughts. bornagain77: (2) under materialism a thinker is an effect caused by processes in the brain. Thinking is the effect. The thinker is the embodied person. bornagain77: (3) in order for materialism to ground rationality a thinker (an effect) must control processes in the brain (a cause). (1)&(2) Same problem as (1). bornagain77: (4) no effect can control its cause. That's false, as any feedback mechanism shows.Zachriel_{March 24, 2016
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ellazimm, what is your response to the simple logic of the following, with which BA77 concluded his post #17 ? '(1) rationality implies a thinker in control of thoughts. (2) under materialism a thinker is an effect caused by processes in the brain. (3) in order for materialism to ground rationality a thinker (an effect) must control processes in the brain (a cause). (1)&(2) (4) no effect can control its cause. Therefore materialism cannot ground rationality. per Box UD It totally undermines your materialism, exposing the 'straw man' constituting your response below. If he is clearly prejudiced, it can only be on the basis of the logic : in which case, it is a mandatory prejudice from the viewpoint of rational thought. 'I don’t argue with non-persons, since all rationality is lost when a person denies he is real.' - BA77 'You are allowed to be prejudiced. But it doesn’t make you right.' - EllazimmAxel_{March 24, 2016
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specter13: http://www.evolutionnews.org/2014/10/the_dog_delusio090751.html
The result is the many genetically and anatomically inferior breeds of our domestic dogs, fully dependent on human care and interest and typically unable to survive in the wild.
The author doesn't know much about dogs apparently. Most dog breeds can quickly become feral. In any case, that an organism may become dependent on humans is just another form of adaptation, similar to how anthropoid primates are dependent on the consumption of vitamin C.Zachriel_{March 24, 2016
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ellazzin: There is ongoing research into that very thing. Hopefully, someday, you’ll have it. Hopefully gold bars are going to fly out of my arse someday. Wake me up when either happens. What about your side? What "side" would that be? Can I say: show me the designer or shut up? I made no claims about any designer.mike1962_{March 24, 2016
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KairosFocus: "PPS: Your point on 3/5 person is historically inappropriate and a classic case of anachronistic misreading. The point at the time was to limit power in Congress of slave holding states in a context where it was not possible in the founding generation to do more than set a 20 year window to close off the slave trade, the low hanging fruit. Notice, the non free persons were recognised as persons." I understand the reason for that clause. But it still assigned a lower human value to some humans. But if you still believe that slavery was not protected by the constitution, how do you explain the following clause? ""No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due."Indiana Effigy_{March 24, 2016
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Origenes #57
To be clear, new information is not generated by the cull. New information is produced solely by blind random non foresighted forces. All the cull does is hamper the ‘search’ of evolution. IOWs by continually removing acquired information the much touted cull (a.k.a. “natural selection”) is lowering the likelihood that blind random non foresighted forces were able to produce/find the fancy stuff that we see in life.
The repeated process of random generated variation, cull, repeat generates new body plans. It's the effect of cumulative selection. Every new generation has more genetic diversity than its parents, those 'selected' from the previous generation. That's more choices for selection to work with. 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.ellazimm_{March 24, 2016
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ellazimm: The cull is not producing information. The new information comes from genetic variation that is generated every generation.
We are in agreement.
ellazimm: Some variants do not make it, information is lost every generation. But new information is also generated.
To be clear, new information is not generated by the cull. New information is produced solely by blind random non foresighted forces. All the cull does is hamper the 'search' of evolution. IOWs by continually removing acquired information the much touted cull (a.k.a. "natural selection") is lowering the likelihood that blind random non foresighted forces were able to produce/find the fancy stuff that we see in life. edit: One more thing. I hold that it is important to make a distinction between the filter of existence and natural selection. By "the filter of existence" I refer to the viability of an organism. If an organism is viable — doesn't fall apart and is self-organizing — it passes the filter of existence. Next there is the randomly whimsical filter of natural selection. It is my impression that there's an equivocation going on between these two.Origenes_{March 24, 2016
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KF & Origenes Start with generation 1, some of them are better able to exploit their environment and resources; some of them are just lucky. Some are 'selected' and some don't survive to reproduce. The breeders have a narrower range of genetic diversity than the whole generation before the 'cull'. Generation 2 is the offspring of those 'selected' in generation 1. Generation 2 has a wider range of genetic diversity than their parents (the breeders of generation 1). Some of that variation is on top of the surviving variations from generation 1. Variation is generated every time offspring are produced. The cull is not producing information. The new information comes from genetic variation that is generated every generation. Some variants do not make it, information is lost every generation. But new information is also generated. And KF, there is no need to re-iterate your argument against a smooth landscape of related life forms. I've heard it many, many times. I know you focus on what you consider 'islands of function' instead of the clear genetic data which shows that all existing life forms share lots of 'information' which pretty clearly indicates that we're all branches of one tree/bush. If you only focus on the ends of the branches (the existing life forms) then they do look like disconnected 'islands of function'. But that doesn't mean there is no path between them. The connecting path goes into the past, sometimes millions of years. A beluga whale and a cockroach have a common ancestor. No one thinks it's sensible to talk about how you would transfer one into the other because that's not how it happened. You continually argue against a strawman, a proposal that no one is making.ellazimm_{March 24, 2016
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ellazimm: You always present your argument as if there is no new variation after a cull.
The reason for this is probably because there is no new variation after a cull — by definition. A cull produces exactly zero new information. Instead all a cull does is removing information. IOWs a cull downsizes the 'search team':
KF: (...) the process is a culler out of varieties and so by definition is a remover of information expressed in the inferior varieties that die out. It is not a creative element, a source of bio information.
I would like to add that removing information is likely to come with a cost. Perfectly viable organisms that may possess unique information for winter time are eliminated during the summer, so to speak.Origenes_{March 24, 2016
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EZ, passed by, the claim of incremental new functional info after cull only works for reasonably smooth hill climbing in a loose sense of that term. The body plan origin issue starting from proteins in AA sequence space up is to FIND islands of coherent function with viable body plans. Credibly requiring 10 - 100+ mn bases of fresh gene info, and on one planet's worth of resources. I do not have a lot of time for long back-forths on tangent after tangent to a point that strikes me as ginned up, blind chance and mechanical necessity DO take in natural selection so called, and also chemical scenarios in Darwin's pond etc, which is the main issue in any case: no root no trunk, branches etc for tree of life models. Show us a solid, empirically grounded case for blind chance and mechanical necessity forming first life and main body plans or else we are looking at ideologically imposed ill founded claims propped up by Lewontin's a priori materialism by the back door of oh, we must use methodological naturalism. Design can create FSCO/I, trillions of cases in point. A von Neumann kinematic self replicator on molecular nanotech in a first cell is FSCO/I. Get us to the root of the ToL on blind chance and mechanical necessity in Darwin's pond or the like backed up by solid observational demonstration of claimed mechanisms, or there is nothing substantial in the ToL claims. KFkairosfocus_{March 24, 2016
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Mapou #32
But even if one assumes a starting point using the most basic replicator, it could not be much simpler than a bacterium.
Why couldn't it be simpler than a bacterium? Again, you are making assumptions and claiming a win.
So evolutionary theorists know (by some magic revelation that they the rest of us idiots are not privy to, I guess) that the initial search was not random? Where is the science in that? Where is the falsifiability? Who or what was directing the search, pray tell? And why should anybody believe evolutionary theorists? What makes them so special? I personally think they are idiots.
Why couldn't it just be chemistry? Have you read some of the (competing) current ideas of how life got started? We may never know exactly what happened but that doesn't mean a bacterium just poofed into existence.
I make it a point to always be rude, contemptuous and disrespectful to all dirt worshippers because this is the way they have treated those who have disagreed with them in the past. This is the way they always treat their critics. In their view, if you are not an atheist, a Darwinist or a materialist, you are an idiot or a stupid creationist.
If I used language on this thread as you do I'd be called for it. You are given special leeway for some reason. Also, I never behaved the way you are complaining about so why do you treat me that way?
We saw an example of that during the recent debate with that jackass/crackpot/ignoramus, Lawrence Krauss. You people need to get a taste of your own medicine. And you will get it. You are stupid as dirt.
You are biased and prejudice. And the moderators let you get away with it. KF #33
so if culling — subtraction of variation — in part driven by differential reproductive success is non random, does it not then come under not logical [If A then B must hold . . . ] but instead mechanical, blind . . . as in, non foresighted . . . necessity? (I leave off the random, stochastic aspects of such differential success.)
There is 'new' variation at every generation. You always present your argument as if there is no new variation after a cull. And selection continues on each new batch of variants. Also, why do you not call Mapou on his attitude and language? Why is he allowed to be incredibly rude and disrespectful. You wouldn't let me behave the way he does. Why the double standard? Mike1962 #34
Show me the initial replicator. Or else shut up.
There is ongoing research into that very thing. Hopefully, someday, you'll have it. What about your side? Can I say: show me the designer or shut up?ellazimm_{March 23, 2016
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S13, good link, thanks. KFkairosfocus_{March 23, 2016
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IE, ARTIFICIAL selection is a design mechanism. There is some part where that turns on often small mutations (mouth of bulldog, say) but often it is breeding out to limits of an existing genetic range. Yes, it is often used as a basis for an argument by analogy that natural circumstances can do the same but the issue in serious discussion is at body plan origin level. The challenge being, islands of function isolated in large configuration spaces. Where given scope of possible configs vs scope of available resources the intervening seas of non function are not credibly span-able. This starts with isolation of clusters of functional [truly functional in vivo] proteins in amino acid sequence space. At say 150 aa, isolation has per investigation been put at something like 1 in 10^70. Cf this for a discussion of some issues. Likewise, this addresses the but dogs show macroevo claim, as was pointed out to you above. Notice the clip from Gieffers: >>On the basis of research of many experts in the relevant fields, Loennig proves that the enormous variability of our domestic dogs essentially originated by reductions and losses of functions of genes of the wolf.>> Also, Behe: >>Dr. L?nnig shows forcefully that one of the chief examples Darwinists rely on to convince the public of macroevolution -- the enormous variation in dogs -- actually shows the opposite. Extremes in size and anatomy come at the cost of broken genes and poor health. Even several gene duplications were found to interfere strongly with normal growth and development as is also often the case in humans. So where is the evidence for Darwinian evolution now?>> There's more, gotta go. KF PS: Not a lot of time to spend on this given current local matters (and a higher priority issue going a-begging), I suggest you scroll up, click the Resources tab and read the discussions on weak arguments and the glossary. PPS: Your point on 3/5 person is historically inappropriate and a classic case of anachronistic misreading. The point at the time was to limit power in Congress of slave holding states in a context where it was not possible in the founding generation to do more than set a 20 year window to close off the slave trade, the low hanging fruit. Notice, the non free persons were recognised as persons. Try: https://americanvision.org/3918/the-original-constitution-and-the-three-fifths-myth/ as a start.kairosfocus_{March 23, 2016
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Effigy, you're an idiot. See ya.Mapou_{March 23, 2016
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Louis: "You grow up. The Constitution does not embrace slavery. Where did you get this crap?" Maybe it was the part about slaves counting as three fifths of a person. But maybe i read that wrong. The rest of your comment isn't worth commenting on. It is just a childish rant.Indiana Effigy_{March 23, 2016
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You grow up. The Constitution does not embrace slavery. Where did you get this crap? I know a chicken sh!t religion when I see one and Darwinism is the worst chicken feather voodoo religion of them all. They deserve nothing but contempt. They deserve to be insulted daily. Anybody who believes that life sprung out of dirt is a religious moron. He or she should not be indoctrinating our kids with their nonsense. It is against the law.Mapou_{March 23, 2016
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Sorry Mapou, but I could care less about your constitution. It also embraces slavery. Not something to be proud of. And the idea of evolution being a religion is just absurd. I may not agree with it but they seem to be able to defend their position without resorting to calling us dirt worshippers. Please grow up.Indiana Effigy_{March 23, 2016
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Effigy, I don't care what you're glad about. The constitution says religion should not be taught in the schools because that would violate the separation of Church and State. And yet the Darwinist dirt worshippers are doing just that with impunity. They should all be locked up for violating the people's constitutional rights. There should be no dirt worshipping religion in our schools. If you believe that dirt is the mother of life, you are a religionist moron and you should be kicked out of our schools, prosecuted for fraud and jailed. Live with it.Mapou_{March 23, 2016
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Louis: "And yes they deserve to be thrown in jail until they recant their false religion that they have imposed on the public." Praise the Lord that you never gain power in any meaningful way. Hitler comes to mind.Indiana Effigy_{March 23, 2016
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Effigy:
I hope that you are not being serious. The idea of throwing people in jail for their ideas is communist and anti-Christian. If you are serious about this then you are in some pretty evil company.
Man, pack it where the sun does not shine. I am nobody's dog and I mean exactly what I say. I resent people using the threat of government force to indoctrinate my children without my consent. Especially in a supposed democracy. And yes they deserve to be thrown in jail until they recant their false religion that they have imposed on the public.Mapou_{March 23, 2016
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