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John Maynard Keynes thought that most economic decision-making occurs in ambiguous situations in which probabilities are not known. He concluded that much of our business cycle is driven by fluctuations in “animal spirits,” something in the mind – and not understood by economists.
Of course, the problem with economics is that there are often as many interpretations of any crisis as there are economists. An economy is a remarkably complex structure, and fathoming it depends on understanding its laws, regulations, business practices and customs, and balance sheets, among many other details.
Yet it is likely that one day we will know much more about how economies work – or fail to work – by understanding better the physical structures that underlie brain functioning. Those structures – networks of neurons that communicate with each other via axons and dendrites – underlie the familiar analogy of the brain to a computer – networks of transistors that communicate with each other via electric wires. The economy is the next analogy: a network of people who communicate with each other via electronic and other connections.
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Scholars can become so trapped in their methods – in the language and assumptions of the accepted approach to their discipline – that their research becomes repetitive or trivial.
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Then something exciting comes along from someone who was never involved with these methods – some new idea that attracts young scholars and a few iconoclastic old scholars, who are willing to learn a different science and its different research methods.
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The claims that the ultra-rich 1% make for themselves – that they are possessed of unique intelligence or creativity or drive – are examples of the self-attribution fallacy. This means crediting yourself with outcomes for which you weren't responsible. Many of those who are rich today got there because they were able to capture certain jobs. This capture owes less to talent and intelligence than to a combination of the ruthless exploitation of others and accidents of birth, as such jobs are taken disproportionately by people born in certain places and into certain classes.
The findings of the psychologist Daniel Kahneman, winner of a Nobel economics prize, are devastating to the beliefs that financial high-fliers entertain about themselves. He discovered that their apparent success is a cognitive illusion. For example, he studied the results achieved by 25 wealth advisers across eight years. He found that the consistency of their performance was zero. "The results resembled what you would expect from a dice-rolling contest, not a game of skill." Those who received the biggest bonuses had simply got lucky.
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traders and fund managers throughout Wall Street receive their massive remuneration for doing no better than would a chimpanzee flipping a coin. When Kahneman tried to point this out, they blanked him. "The illusion of skill … is deeply ingrained in their culture."
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In a study published by the journal Psychology, Crime and Law, Belinda Board and Katarina Fritzon tested 39 senior managers and chief executives from leading British businesses. They compared the results to the same tests on patients at Broadmoor special hospital, where people who have been convicted of serious crimes are incarcerated. On certain indicators of psychopathy, the bosses's scores either matched or exceeded those of the patients. In fact, on these criteria, they beat even the subset of patients who had been diagnosed with psychopathic personality disorders.
The psychopathic traits on which the bosses scored so highly, Board and Fritzon point out, closely resemble the characteristics that companies look for. Those who have these traits often possess great skill in flattering and manipulating powerful people. Egocentricity, a strong sense of entitlement, a readiness to exploit others and a lack of empathy and conscience are also unlikely to damage their prospects in many corporations.
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it may be better to think of the return to education as stochastic. Education not only increases the average income a person will earn, but it also changes the entire distribution of possible life outcomes. It does not guarantee that a person will end up in the top 1 percent, but it increases the likelihood. I have not seen any data on this, but I am willing to bet that the top 1 percent are more educated than the average American; while their education did not ensure their economic success, it played a role.
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Visualisations like the graph in figure 1 can enliven information, grab people's attention, inspire, and influence. They can summarise data concisely, illuminate hidden patterns, and provide instruction for those with poor numeracy. Many graphics have these features, but those used to represent probabilities may be of particular importance when the information is complex and the circumstances highly significant.
The complex set of probabilities in the mammography test question is explained simply and attractively in figure 1, which guides you through the logic necessary to dissect the problem. This figure has many desirable properties. It is clear and free from clutter. The icons are suggestive, and are labelled with numbers and words. A natural choice of population size, namely 1000, ensures the arithmetic is simple, and all outcomes of the test are considered. Finally, and importantly, the graphic is accompanied by a narrative, which describes how to interpret the data.
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There is one obvious difference between the past and present sea battle – namely that there is nothing ongoing in the past sea battle. Everything about the battle – when it started, how long it lasted, how many ships were involved and their exact trajectories, how much blood was spilt, not to speak of the outcome – is settled. When and only when the battle is over, completed – when it enters the past – is it a definite item: Event E. So long as the battle is present, that is to say ongoing, it is not E: it is the opening part of a sea battle.
This falling short of being E is even more obvious in the case of an event that is still future. We can express this in the traditional way by saying it is indeterminate. This indeterminacy will extend to the very possibility of the battle taking place at all.
We are now in a position to see what is wrong with McTaggart’s starting point. It is a mistake to think of the sea battle E as the same thing passing through three phases – Phase One when it is E (future), Phase Two when it is E (present), and Phase Three when it is E (past). There is no such thing, an identical event E, that has that succession of tensed properties – futurity, presence, and pastness – that are incompatible (as McTaggart argues). E (future) is not the same as E (present), which is not the same as E (past). E (future) is a mere possibility, whose characteristics are yet undetermined (irrespective of whether it subsequently takes place); E (present) is a combination of a portion of the complete event E and its possible continuations or completions; and E (past) is the complete event. There is therefore nothing like a tense tourist E visiting future, present and past in succession – never mind occupying them all at once.
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why do many intelligent people (including McTaggart) imagine that believing in tensed time requires you to believe in the same item, event E, visiting the three tenses in turn, as a result of which it runs the risk of having to inhabit more than one tense at once (as McTaggart pointed out)? It is partly because we use the same kind of expression when we refer to an event in the future, in the present, and in the past: we refer to ‘tomorrow’s sea battle’ that does take place just as we refer to ‘tomorrow’s battle-averting treaty-signing’ that, as it turns out, does not take place. This similarity of referring expression in the two cases conceals the profound difference between them – between a mere possibility, whose content is entirely dependent on how it is entertained, imagined, or anticipated, and is only an ‘honorary event’, and an actuality, whose content is in the real world, determinate in every detail – including those millions of details no-one has imagined or anticipated.
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In its AR4 report the IPCC says:
The uncertainty guidance provided for the Fourth Assessment Report draws, for the first time, a careful distinction between levels of confidence in scientific understanding and the likelihoods of specific results. This allows authors to express high confidence that an event is extremely unlikely (e.g., rolling a dice twice and getting a six both times), as well as high confidence that an event is about as likely as not (e.g., a tossed coin coming up heads). Confidence and likelihood as used here are distinct concepts but are often linked in practice.
Here are some specific definitions to help you answer some questions.
A. "high confidence" means "about 8 out of 10 chance of being correct".
B. "extremely unlikely" means "less than 5% probability" of the event or outcome
C. "as likely as not" means "33 to 66% probability" of the event or outcome
So here are your questions:
1. If the IPCC says of a die that it has -- "high confidence that an event is extremely unlikely (e.g., rolling a dice twice and getting a six both times)" -- how should a decision maker interpret this statement in terms of the probability of two sixes being rolled on the next two rolls of the die?
2. If the IPCC says of a die that it has -- "high confidence that an event is about as likely as not (e.g., a tossed coin coming up heads)" -- how should a decision maker interpret this statement in terms of the probability of a head appearing on the next coin flip?
Please provide quantitative answers to 1 and 2, show your work.
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There is insufficient information to do the calculation rigorously. Actual calculation would require assignment of the rest of the second-order probability (the "confidence") to different probability distributions.
In the absence of that information, a reasonable decision-maker might
(a) decide to ignore the second-order probability and use the existing PDFs ("extremely unlikely" for double sixes and "as likely as not" for the coin toss
(b) hedge against incorrect estimates of the "true" probabilities by assigning additional likelihood to "tail" events. In the coin toss event this doesn't really matter - if you only have two possible outcomes that are approximately equally likely, being somewhat wrong about the PDF won't make much difference for planning. But if you have reason to worry that an event someone called "extremely unlikely" might actually be just "unlikely", you might want to invest extra in hedging against it. (As well, of course, as extra research).
This just returns to my more general claim, that the issue for decision-makers is deciding what PDF to act "as if" is the "true" PDF, even when there really is no "true" PDF. -
-1-Paul Baer
Thanks ... I agree with this answer, and have these thoughts about the implications:
(a) ignore the second order stuff (the IPCC generally does) -- bad idea, as this means ignoring potentially relevant info (see #3 below)
You write: "the issue for decision-makers is deciding what PDF to act "as if" is the "true" PDF, even when there really is no "true" PDF"
As I said on the other thread, I get what you are saying, but I have a hard time translating this to practical situations. I think that the decision calculus has to factor in what it means to be "wrong" in a probability judgment as related to the outcomes of a decision based on such judgments. Expressing the view that such judgments cannot be "wrong" is not the way to go.
I return to the notion that context matters in such judgments and flipping a coin has little in common with ratings of mortgage-backed securities.
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Deep in the comments on an earlier thread Paul Baer offers the following hypothetical:
In my statistics class, I ask my students "what is the probability that when I flip this coin, it will land heads." (And yes, assume it's a fair coin.)
Of course they answer 50% or some equivalent.
Then I flip it and hold it covered on the back of my hand. Then I ask, "What is the probability that this coin is heads." There's usually some puzzlement. Someone says "50%". And I say, "but either it's heads or it isn't. How can there be a fifty percent chance it's heads?"
Then I ask "what odds would you give me if I bet that it's not heads?" Eventually those who know what betting odds mean understand the point. Even when something has happened (like, the deck has been shuffled and the card that will be dealt could be known under some epistemic conditions DIFFERENT FROM OURS) we have to ACT as if the odds are, well, what we think they are. -
To which I responded:
Consider the following case:
Answers gladly accepted.
You flip a coin in your class and ask for the probability of a head. A savvy student replies:
[S1]: The odds of a head are 50-50
You then reveal to the class that the coin is not fair, in fact there is a 75% chance of a tail. You ask the student, now what are the odds of a head? (All while the flipped coin sits on your hand)
The student now replies:
[S2] The odds of a head are 25%.
Q1. Now would it be fair to say that [S1] was incorrect? - 1 more annotation(s)...
Jonassen, R. and R. Pielke, Jr., 2011. Improving conveyance of uncertainties in the findings of the IPCC, Climatic Change, 9 August, 0165-0009:1-9, http://dx.doi.org/10.1007/s10584-011-0185-7.
Abstract Authors of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) received guidance on reporting understanding, certainty and/or confidence in findings using a common language, to better communicate with decision makers. However, a review of the IPCC conducted by the InterAcademy Council (2010) found that "the guidance was not consistently followed in AR4, leading to unnecessary errors . . . the guidance was often applied to statements that are so vague they cannot be falsified. In these cases the impression was often left, quite incorrectly, that a substantive finding was being presented." Our comprehensive and quantitative analysis of findings and associated uncertainty in the AR4 supports the IAC findings and suggests opportunities for improvement in future assessments.
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If we confine our attention to those findings that refer to the future, one can ask how many IPCC findings can be expected to become verified ultimately as being accurate? For example, if we consider findings that refer to future events with likelihood in the ‘likely’ class (i.e., >66% likelihood) then if these judgments are well calibrated then it would be appropriate to conclude that as many as a third can be expected to not occur. More generally, of the 360 findings reported in the full text of WG1 across all likelihood categories and presented with associated measures of likelihood (i.e., those summarized in Table 2 below), then based on the judgments of likelihood associated with each statement we should logically expect that about 100 of these findings (~28%) will at some point be overturned.
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ur paper concludes:
Although the IPCC has made enormous contributions and set an important example for global assessment of a vexing problem of immense ramifications, there remain clear opportunities for improvement in documenting findings and specifying uncertainties. We recommend more care in the definition and determination of uncertainty, more clarity in identifying and presenting findings and a more systematic approach in the entire process, especially from assessment to assessment. We also suggest an independent, dedicated group to monitor the process, evaluate findings as they are presented and track their fate. This would include tracking the relationship of findings and attendant uncertainties that pass up the hierarchy of documents within AR5. Strict rules for expressing uncertainty in findings that are derived from (possibly multiple) other findings are needed (see, e.g., the second example in the Supplementary Material).
It is not the purpose of this note to discuss other, related scientific assessments of climate change knowledge; but, we do note that our preliminary analysis of the U.S. Global Change Research Program Synthesis and Assessment Products suggests a far less systematic application of the guidance supplied to authors of those documents and far less consistent application of the defined terms. We believe that the concerns we have expressed here, and the resulting recommendations, apply more broadly than the IPCC process. - 12 more annotation(s)...
Imagine that you are a contestant on the classic television game show Let’s Make a Deal. Behind one of three doors is a brand-new automobile. Behind the other two are goats. You choose door number one. Host Monty Hall, who knows what is behind all three doors, shows you that a goat is behind number two, then inquires: Would you like to keep the door you chose or switch? Our folk numeracy—our natural tendency to think anecdotally and to focus on small-number runs—tells us that it is 50–50, so it doesn’t matter, right?
Wrong. You had a one in three chance to start, but now that Monty has shown you one of the losing doors, you have a two-thirds chance of winning by switching. Here is why. There are three possible three-doors configurations: (1) good, bad, bad; (2) bad, good, bad; (3) bad, bad, good. In (1) you lose by switching, but in (2) and (3) you can win by switching. If your folk numeracy is still overriding your rational brain, let’s say that there are 10 doors: you choose door number one, and Monty shows you door numbers two through nine, all goats. Now do you switch? Of course, because your chances of winning increase from one in 10 to nine in 10. This type of counterintuitive problem drives people to innumeracy, including mathematicians and statisticians, who famously upbraided Marilyn vos Savant when she first presented this puzzle in her Parade magazine column in 1990.
Even a strong argument from purely factual premises is open to refutation unless we are assured that it has taken account of all relevant facts. Realistically, of course, we can never be sure that we have taken account of all relevant facts, especially with an issue as complex as a national budget. But a good inductive argument requires getting as close as we can to this ideal.
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The answer lies in a crucial distinction between deductive and inductive reasoning. In a deduction (e.g., all humans are mortal; Socrates is human; therefore, Socrates is mortal), the truth of the premises logically requires the truth of the conclusion. If the premises are true, the conclusion must be true. Adding further premises that might seem relevant to the conclusion (e.g., Socrates is very young and there will be major medical advances before Socrates reaches old age) will make no difference to the conclusion.
In an inductive argument (e.g., Most humans do not live for 100 years; Socrates is human; therefore, Socrates will not live for 100 years), the premises only make the conclusion probable. As a result, adding further premises can alter the force of the argument. For example, if Socrates is 99 years old and in very good health, it is probable that he will live to be 100.
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As is inevitable in almost all discussions of complicated political topics, Taylor and his critics are employing inductive arguments. Therefore, their reasoning is open to question simply by adducing further relevant facts such as pointing out the aging of our population and increases in medical costs, or noting that there could be serious reform of the structure of our welfare system.
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From MIT’s Technology Review:
In practice, there are numerous examples of democratic systems that are rife with corruption or paralysed by disagreement. Even in benign parliaments, it is often an open question as to whether the work they do really benefits the majority of people.
Today, Alessandro Pluchino and amici at the Universitá di Catania in Italy say there is a better way. They have modelled the behaviour of a two-party parliament and examined how it changes as randomly selected independent legislators are introduced into the system. Their counterintuitive conclusion is that randomly selected legislators always improves the performance of parliament and that it is possible to determine the optimal number of independents at which a parliament works best.
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The researchers wanted to know from a mathematical perspective, if adding a random distribution of ‘politicians’ would increase the number of acts that got passed — and if those acts were socially beneficial. So, the “measure of performance is the number of acts passed multiplied by their average social benefit.” They expected to see the number of socially-beneficial acts passed increase as more ‘random politicians’ were added to the mix. And sure enough:
“They ran their model for various distributions of power in the two party system and found that in every case, adding random legislators improves the performance of parliament.”
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if it was a civic duty to act as legislator, if you were randomly selected to do so (like a draft for governance) — and left office after a term without having to cater to corporate interests to drum up campaign finances for reelection. It would give us a way to sidestep the tightening grip that corporations and the wealthy have on our politics. Sure, there would be some lazy, incompetent people selected who would act in their own self-interest or against the societal good. But as Pluchino’s work shows, they’re offset by smarter ones, willing to work for the good of society.
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Whenever confronted with a new claim, it’s reasonable to think that the null hypothesis is that the claim is not true. That is, the default position is one of skepticism. Now the tricky part is that type I and type II errors are inversely proportional: if you lower your threshold for one, you automatically increase your threshold for the other (there is only one way out of this trade-off, and that’s to do the hard work of collecting more data). So if you decide to be conservative (statistically, not politically), you will raise the bar for evidence, thereby lowering the chances of rejecting the null hypothesis and accepting the new belief when it is not in fact true. Unfortunately, you are also simultaneously increasing your chances of accepting the null and rejecting the new belief when in fact the latter is true.
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A type I error is the one you make if you reject a null hypothesis when it is in fact true. In medicine this is called a false positive
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A type II error is the converse: it takes place when one accepts a null hypothesis which is in fact not true.
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Free Will: Children and the Scientific Worldview
How kids know the monster under the bed isn’t real (06:22)
Experiments probe causal thinking in children (09:05)
Do scientists have more in common with kids than other adults? (06:30)
Are morality and causality intertwined for ordinary people? (14:23)
4-year-olds’ value-laden perspective on others’ intentions (07:40)
Are Pinker and Chomsky dead-wrong about child development? (03:41)
There are many sources of potential artifact in the climate data. Where are the temperature stations located? Have cities built up near them over the years, leading to false warming? There are also artifacts in the time it takes for stations to report their data to central repositories, which then have to crunch the data. There are changing methods of temperature measurement of the years.
In addition to artifact in the gathering and reporting of the data, there are numerous trends in the data itself. There are multiple natural climate cycles, as well as short term anomalies (like volcanic eruptions) that need to be taken into account.
This is why sorting through all of this noise in the climate data is not for the amateur. Of course, now that climate change is a politically-charged issue, the internet if full of exactly that – amateur analysis of the data. This is definitely an area where substituting one’s own analysis for the consensus of scientific opinion is probably not a good idea.
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data may contain spurious patterns or results, depending on the methods used to gather that data.
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There are many kinds of false patterns in data other than sampling bias, and it often takes an expert to know how to interpret a complex data set. Meanwhile complex data can be presented to the public in a partial or deception way in order to create a false impression. The global warming controversy is now the poster child for this phenomenon. The notion that the planet is slowly warming and that human activity is playing a significant role is based upon large sets of data that has to be analyzed in very complex and subtle statistical ways. Both sides of the controversy point to biases or errors in the data that falsely make it look as if the Earth is or is not warming.
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you have probably not run into many humble economists. By its nature, punditry craves attention, which is easier to attract with certainties than with equivocation.
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certitude reflects bravado more often than true knowledge.
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In 1967, Milton Friedman gave an address to the American Economic Association with this simple but profound message: The inflation rate that the economy gets is, in large measure, based on the inflation rate that people expect. When everyone expects high inflation, workers bargain hard for wage increases, and companies push prices higher to keep up with the projected cost increases. When everyone expects inflation to be benign, workers and companies are less aggressive. In short, the perception of inflation — or of the lack of it — creates the reality.
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“A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined.” (David Hume, On Miracles)
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it is Easter weekend, and even National Public Radio had to broadcast some cheesy story about religion. Even so, I was not prepared for the amount of sheer nonsense that I heard from Barbara Bradley Hagerty over at Morning Edition.
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in a study released on Thursday, the folks at the Ochs Center for Metropolitan Studies in Chattanooga, Tenn., decided to take an in-depth look at the promises made by purveyors of new coal plants.
Their findings seem to suggest that the trade-off that many cash-strapped communities make — specifically, accepting the health and environmental risks that come with having a new coal-burning power plant in their midst, in return for a boost in employment — is not what it’s cracked up to be.
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The analysis looked at the six largest new coal-fired power plants to come online between 2005 and 2009, including facilities in Pottawattamie County, Iowa; Milam and Robertson Counties, Tex.; Otoe County, Neb.; Berkeley County, S.C.; and Marathon County, Wisc. All were plants exceeding capacity of 500 megawatts.
Researchers combed through each project’s initial proposals and job projection data, including public statements, published documents and other material. They then set about taking the pulse of employment — before, during and after construction — in the areas where the projects were built, relying chiefly on the Bureau of Labor Statistics’ Quarterly Census of Employment and Wages.
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The big idea: Even accounting for other ups and downs in employment activity in these counties, projects of this magnitude should stand out amid the data din, permitting some ground truthing of the coal projects’ actual impact on the local economy.
The results: only a little over half, or 56 percent of every 1,000 jobs projected, appeared to be actually created as a result of the coal plants’ coming online. And in four of the six counties, the projects delivered on just over a quarter of the jobs projected.
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Currently, the public views genes primarily as self-contained packets of information that come from parents and are distinct from the environment. “The popular notion of the gene is an attractive idea—it’s so magical,” said Mark Blumberg, a developmental biologist at the University of Iowa in Iowa City. But it ignores the growing scientific understanding of how genes and local environments interplay, he said.
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With the rise of molecular biology in the 1930s and genomics (the study of entire genomes) in the 1970s, scientists have developed a much more dynamic and complex picture of this interplay. The simplistic notion of the gene has been replaced with gene-environment interactions and developmental influences—nature and nurture as completely intertwined.
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Evolution and the fear of chance.
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people can't stomach the theory of natural selection is that they hate the idea that everything we see around us is the result of blind chance. Hostility to the notion of chance is certainly a recurrent theme in creationist objections.
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evolution by natural selection is not really evolution by chance, as the creationists claim. But even so chance does play a role. Stephen Gould, in many of his essays, repeatedly drove home the importance of chance (or rather, contingency) in evolution
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