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Dictionary definition of random:
Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard
A pseudorandom process is a process that appears to be random but it is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process.
Definition: Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones.
Sometimes the digits in the decimal expansions of irrational numbers are used in an attempt to obtain random numbers. Most whole numbers have irrational square roots, so entering a string of six or eight digits into a calculator and then hitting the square root button can provide a sequence of digits that seems random. Other algorithms have been devised that supposedly generate random numbers. The problem with these methods is that they violate condition (2) in the definition of randomness. The existence of any number-generation algorithm produces future values based on past and/or current ones. Digits or numbers generated in this manner are called pseudorandom.
Statisticians, mathematicians, and scientists have long searched for the ideal source of random numbers. One of the best methods is the sampling of electromagnetic noise. This noise, generated by the chaotic movements of electrons, holes, or other charge carriers in materials and in space, is thought to be as close to "totally random" as any observable phenomenon.
As far as I am aware, nobody has ever given an entirely convincing definition of the term `random sequence'. On the other hand, everybody has a common-sense idea of what it means. We say things like: `the sequence should have no pattern or structure'. More directly we might say that knowing x1,..., xn tells us nothing about xn + 1,....
Definition 5.2 A sequence [xk] on [0, 1) is n-distributed on [0, 1) if the sequence [pk] given by
pk = (xkn, xkn + 1,..., xkn + n - 1) [0, 1)n
is uniformly distributed on [0, 1)n.
We will require that a random sequence in [0, 1) be (infinity) -distributed on [0, 1), i.e. k-distributed for all k.
This turns out to be an inadequate definition of randomness, but it is good enough for all practical purposes. In particular, an -distributed sequence will pass all the standard statistical tests for randomness. (If you want to be thoroughly perverse you could argue that the fact that it passes all such test is itself evidence of a certain non-randomness!)
No human investigation can be called real science if it cannot be demonstrated mathematically.
Leonardo da Vinci
Infinity (symbolically represented by ∞) is a concept in mathematics and philosophy that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity.
In mathematics, there must be an infinite expansion of information for randomness to exist.
When you look at the definition of random, it is hard to imagine that it has possibly been part of the process, connected to the development of all life on Earth.
Definition: Random numbers are numbers that occur in a sequence....
I’m no expert in understanding the mathematics involved in the above equations, but with phrases like, “nobody has ever given an entirely convincing definition of the term `random sequence' and “This turns out to be an inadequate definition of randomness”, I’m not convinced!
Summary:
1) “Pseudorandomness”, incorporates a designed mathematical formula, to produce a pattern of numbers, that appear to be random, but are not.
2) Infinity is a concept, not yet proven.
3) Without infinity, “Pure Randomness” does not exist.
4) “Pure Randomness” has yet to be accurately demonstrated mathematically.
Originally posted by Welfhard
The appearance of design does not mean design.
Originally posted by Welfhard
And indeed when you look at all the lineages that appear and go extinct, the ebb and flow of constantly altering forms of life begin to appear to behave in an unguided and purely reactionary way but that's because of natural selection, not mutation.
Originally posted by Welfhard
Numbers, not mutations. Biology isn't maths.
Originally posted by Welfhard[/I]
Random mutations fulfil the first definition of random, not the mathematical one because evolution isn't arithmetic.
Originally posted by Welfhard[/I]
The only way numbers relate to evolution is in simulations, they do not dictate real life.
Originally posted by Welfhard[/I]
So you think that reality is obliged to conform to the limitations of our language?
Originally posted by Joecroft[/I]
Summary:
1) “Pseudorandomness”, incorporates a designed mathematical formula, to produce a pattern of numbers, that appear to be random, but are not.
2) Infinity is a concept, not yet proven.
3) Without infinity, “Pure Randomness” does not exist.
4) “Pure Randomness” has yet to be accurately demonstrated mathematically.
Originally posted by Welfhard[/I]
None of that has anything to do with evolution and genetic mutations.
Originally posted by Welfhard[/I]
Mutations are "random" in the same sense that the pattern that forms in sand when you throw it across a table is random - you can't predict it nor would you bother & you know it all comes down to circumstance. Such a pattern doesn't conform to a desire outside of you throwing it across a table.
Originally posted by Welfhard[/I]
This is randomness in a practical sense, no one is suggesting that "random" mutations defies the law of causality.
One of the classic arguments for the existence of God is known as the "Cosmological argument" or "First cause" argument. It works from the premise that every natural event is the effect of a cause. If this is so, then the events that caused today's events must have had causes themselves, which must have had causes, and so forth. If the chain never ends, then one must uphold the hypothesis of an "actual infinite", which is often regarded as problematic, see Hilbert's paradox of the Grand Hotel. If the chain does end, it must end with a non-natural or supernatural cause at the start of the natural world -- e.g. a creation by God.
Despite this non-random distribution, scientists believed for many years that these so-called mutational hotspots were the product of natural selection and other post-mutational processes, and that the mutations occurred at random. However, "in last two decades, the large amount of both genomic and polymorphic data has changed the way of thinking in the field," Dacheng Tian of Nanjing University in China, who did not participate in the work, wrote in an email to The Scientist. "[This] idea provides a self-increasing hypothesis, which may be useful to rethink the formation of such non-randomness."
Using SNP data from the HapMap website for human chromosome 1, Amos calculated the average size and density of existing mutational clusters. He then ran simulations under the assumption of either this new, non-random mechanism of mutation formation or that of randomly occurring mutations. He found that the non-random model more closely predicted the frequency and density of the mutational clusters on the chromosome……………………
…………"My theory is going to shake things up majorly," Amos said. "The concept of non-independent mutations simply wasn't thought of before -- this is completely new and it really changes how we think of DNA evolving."
Your random analogy of throwing the sand, is not “pure randomness”, because there is an exact number of possibilities in which the sand can land on the table, albeit an extremely large number but it is a finite number nonetheless. The only way it could be classed as “pure random” is if you threw an infinite amount of sand.
Cosmological argument
Dictionary definition of random:
Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard
Originally posted by Welfhard[/I]
The first cause doesn't have to obey for one reason. Without time, there is no causality.
Originally posted by Welfhard[/I]
"Random" mutations are blind and unwilled by anything and are in a particle sense random.
Originally posted by Joecroft[/I]
Dictionary definition of random:
Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard
Originally posted by Welfhard[/I]
Random mutations fulfill the dictionary definition of random.
Originally posted by Welfhard[/I]
Randomness in math may be theoretically impossible but that's a different definition or random (could even be said to be a different word) unique to mathematics. Biology has nothing to do with it.
So without time and no causality, how do you propose things got started?
The will of a particular species, is one factor that has an impact on its evolutionary development.
How can “Random” mutations be blind and unwilled by anything, considering that a species interacts with its environment and other species, which in turn has an effect on its evolution at a cellular level?
How many living things, do you know; don’t have an aim, are not guided in any way or in any particular direction and don’t make any conscious choices in any form, what so ever?
So both definitions are closely connected.
Originally posted by Welfhard[/I]
How the hell should I know? There's no way to know what's beyond the bigbang.
Originally posted by Welfhard[/I]
The most will can influence is natural selection (ie. selective breeding) but mutations appear at a steady rate allowing new diversity.
Originally posted by Welfhard[/I]
Do you think either you or your mother had any intentional influence on the approximate 150 mutations that you carry? (that's the going rate for each new child)
Originally posted by Welfhard[/I]
But their mutations occur in spite of their aim. They have no control over the mutations that occur when they do.
Originally posted by Joecroft[/I]
So both definitions are closely connected
Originally posted by Welfhard[/I]
But also have very different implications in mathematics as compared with biology.
Originally posted by Welfhard[/I]
I hate this thread. I hate arguing semantics as if it has any bearing on the real word when it doesn't'.
Our whole discussion so far about “random mutation” has boiled down to you saying “How the hell should I know?”, I mean, at least if you believed in a causal loop/infinity, you would have some reason to accept “random mutation”, but even then, it couldn’t be said to be a fact.
If we look at the actual mutation process itself, they do appear to happen at a steady rate. If they are happening at a steady rate, can we really say that, that part of the process, is random?
No of course not. But the will of each individual species, does have a bearing on the mutations it carries, over a long period of time. It also has a bearing on the mutations that it doesn’t carry.
The fact that species have an aim, means you can’t say the whole process is completely random IMO.
From my research so far, science is still trying to understand the area of mutation and this is an ongoing study, it is not completely understood.
So to use the phrase “random mutation” is not completely correct because the exact processes connected to mutation, haven’t yet been clearly proven scientifically.
Maybe you hate this thread because it is attempting to point out to you, that the preconceptions of your belief system, might not be true.
or
Maybe you hate this thread because your current logical constructs, lead you to a dead end.
Originally posted by Welfhard[/I]
But that's got nothing to do with the cause of these mutations so is irrelevant. All your saying is that we organisms react in a not-random way to mutations, though that doesn't have any bearing on whether mutations are random or not (unless they've managed to wander into a radiated area of some nature).
Originally posted by Joecroft[/I]
The fact that species have an aim, means you can’t say the whole process is completely random IMO.
Originally posted by Welfhard[/I]
Why not?
Originally posted by Welfhard[/I]
This could be the ol' order from chaos thing. But anyway it's not true; the aim of animals doesn't have influence on the nature of the occurrence of mutations.
Originally posted by Welfhard[/I]
Even if the were, we'd still say mutations were random because random is a useful word to describe the unpredictable. We could know exactly how mutations occur but we'd still be unable to predict them because we would need to be aware of trillions of factors leading up to and causing the failure of a genetic system.
Originally posted by Welfhard[/I]
I hate this thread because it's a pointless debate about semantics and there isn't much more boring.
But you seem to think that because of that we can't use the word random in an every-day-chaos-&-circumstances way that it has some bearing on the nature of biology. We use the word to describe a type of humour or events which are random in the same sense as mutations are random. That's why I hate this thread.
If the will plays a role in evolution, then it will automatically have an impact on future mutations.
Science doesn’t fully understand how mutations work, so any factor being considered that could affect it, is not irrelevant.
Because we don’t fully understand the effects, that the aims of a particular creature might have on it’s own evolution, we can’t say it’s random or non random because it‘s unknown.
There aim might have an influence, but we/you can’t state, that it’s untrue or true because according to scientists, the causes of “random mutations” are unknown.
Random may be a useful word to use but essentially what science is saying is, that it hasn’t yet worked out how it works.
It’s not so much about semantics it’s more about an incorrect usage of words.
It’s when it’s used in science to describe a process that no one fully understands
It would be more intellectually honest for science to say “unknown mutations” or just simply leave it as “mutations.”
Originally posted by Joecroft[/I]
Science doesn’t fully understand how mutations work, so any factor being considered that could affect it, is not irrelevant.
Originally posted by Welfhard[/I]
No it is irrelevant. Random mutations are called random because there's no way to know where in the genome they will appear or when. That's why they're random - how they affect and organism has nothing to do with it.
Originally posted by Welfhard[/I]
Mutations are cause by the same short comings as every biological system does. They're just errors caused by a failer for proteins to recode the letters. That's all.
Originally posted by Welfhard[/I]
Not being able to predict something and not understanding are two totally different things.
Originally posted by Joecroft[/I]
It’s not so much about semantics it’s more about an incorrect usage of words.
Originally posted by Welfhard[/I]
No, it's semantics.
Originally posted by Welfhard[/I]
Science doesn't fully understand anything.
Originally posted by Welfhard[/I]
No random works. It tells us that mutations have simply occurred due to some combinations of circumstantial factors making them just chance.
No, it is potentially relevant; we can’t say it’s irrelevant at this moment in time because science doesn’t know the exact causes of mutation.
Well, in the context of science; scientific experiments are often repeated many times. Once they get to the point where they can predict an experiments outcome, it is generally a good indication, that they have a better understanding of it.
No, it’s not just about semantics.
Sounds like a good title, for a new thread…lol
Do you think that’s a possibility?
Originally posted by Welfhard
Radiation, mutagenic chemicals and circumstantial failures due to imperfections in proteins.
Originally posted by Welfhard
It is semantics because "random mutation" essentially means "unpredictable mutations." It's more universally understandable to say random, ie. the first definition of the word.
Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard
unpredictable [ˌʌnprɪˈdɪktəbəl]
adj
not capable of being predicted; changeable
unpredictability , unpredictableness n
unpredictably adv
semantics [sɪˈmæntɪks]
n (functioning as singular)
1. (Linguistics) the branch of linguistics that deals with the study of meaning, changes in meaning, and the principles that govern the relationship between sentences or words and their meanings
2. (Philosophy / Logic) the study of the relationships between signs and symbols and what they represent
3. (Philosophy / Logic) Logic
a. the study of interpretations of a formal theory
b. the study of the relationship between the structure of a theory and its subject matter
c. (of a formal theory) the principles that determine the truth or falsehood of sentences within the theory, and the references of its terms
Originally posted by Welfhard
A discussion entirely immaterial to evolutionary theory and boring to boot.