Is Success Luck or Hard Work? – YouTube

I like this guy’s videos and certainly endorse the ideas expressed in this one:
But despite his byline he sometimes puts slickness ahead of veritacity and the bit about the astronaut selection model is unfortunately misleading. In the model both skill and luck are assigned by chance and the labelling was arbitrary, so the same argument would work the other way to show that if the selection was based 95% luck and 5% talent then all of the selected would in fact be talented – and more generally in a highly competitive selection process, any factor which contributes 5% to each evaluator’s judgement will turn out to be essentially a prerequisite for selection.

See also ‘The Drunkards Walk’ by Leonard Mlodinow

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Can Virtuality ever substitute for Reality?

The animatronic moose twitched the skin of its flank, and as the flies buzzed off, water drops dripped from the hairs on its belly. Four days into a seven day circuit of the Bowron Lakes, we were in a swampy area where each lake seemed to have a moose or two which appeared off to the left of us as we paddled in from the river, and which bounded off into the woods a moment or two later; and about the third time this happened, on the same day that we had seen an osprey catch a fish and a couple of beavers poking their heads up from the water as we prepared to drag-portage across a dam,  I had joked that it was just like being in Disneyland with all the predictable animatronic displays in each section.

But this time I was nervous. Perhaps we were too close, because if the moose spooked and ran towards us, its hooves might do us more damage than a mere dunking in slightly smelly water.


That was real. But the picture that occupies the header for this Aeon/Psyche article gave me the tools to imagine an experience I have never had. Having paddled a kayak in ocean waters, and having seen ponds in glacial ice up close, I could already well imagine the experience of paddling up to a floating iceberg – and maybe into and over the slightly luminous pale turquoise of the shallow water between the two looming mounds of hard white ice (rendered completely opaque by the action of weathering on its sometimes smoothly puckered and sometimes ornately sculpted surface). And prompted by the picture (or by a verbal description) I could even imagine the concern I might have on looking up at the darkening sky – about whether I should cut my visit short for fear of being caught far from land in bad weather.

Of course, that imagined fear is different (at the time) from the real fear I felt about getting too close to the moose. But I am not sure that the memory of it is necessarily so much different (which may be why false memories of abuse can sometimes be as harmful to the victim as the reality). And the same applies to almost every aspect of every other travel experience I have had. We do not now have (and may never have!) the technology needed to create a truly immersive travel experience. But if we did, and if that experience could include interactions with real people (or avatars that we could not distinguish from such), so that ethical decisions about how much to tip and so on would be understood to have real consequences for other real people, then I am not sure that anything would be lost by replacing all travel with its virtual counterpart.

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Another Rant About “scientism”

Quora: Alan Cooper’s answer to What is scientism? Why was Lewis against it?

The word “scientism” by its structure should refer to the belief system of a scientist, but it has been dishonestly appropriated by a bunch of religious philosophers to refer to a kind of worship of science as the only source of answers to anything – including questions of ethics and value (about which as yet science makes no claims).

A more honest name for that uncritical worship of science would have been “scienceism” and its followers could be called “scienceists” rather than scientists (who are practitioners of science, rather than believers in its exclusive power to answer all our questions). So I think that the wrong word was used deliberately in order to gain an advantage in arguments with scientists by subtly creating an impression that they all believe something that many do not.

[This may seem like an unfair claim, but I am disinclined to give the “scholars” who introduced the term much benefit of the doubt as they were just the kind of language specialists who, if not completely stupid, could not have failed to notice the problem with that word choice.]

C.S.Lewis (who was not the originator of that duplicitous naming game) was against scienceism for the very good reason that there are many questions we can ask which do not have empirically testable answers.

“What is ‘good’?” or even “What should I do next?” are questions to which the answers depend on the evaluation of competing claims, whose relative importance at any particular time may depend on many things from the community to the brain chemistry of the questioner, and for which we have no foreseeable means of definition and measurement.

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Book Review: ‘Time for Socialism,’ by Thomas Piketty – The New York Times

According to the New York Times’ Book Review of ‘Time for Socialism,’ by Thomas Piketty ,

Piketty calls for a “universal capital endowment” for all citizens beginning at birth, funded by taxes on wealth and inheritances.


Though provocative, none of these ideas is remarkable or original.

Well I am sure the idea wasn’t original with me either. But what is remarkable (to me) is the lack of a strong movement arguing for this for decades.


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Rediscovering Hegel

Rediscovering Hegel is not something I particularly want to do. But I did find this article quite interesting and it struck me as a good example of what I can appreciate about academic Philosophy. I do enjoy considering how people have struggled to express their ideas about the mental process and its implications. And I do think that people who have thought about this more seriously than I can be useful members of deliberative bodies such as “ethics boards” and so on. But their value to me is in the process of facilitating mutual understanding as a result of long exposure to how subtle differences in language use can lead to unnecessary conflict, rather than as arbiters of what is morally correct or scientifically valid. And many philosophers (or at least those advocating for their inclusion, or responding to people like Weinberg, Feynman, and Hawking) seem to get this wrong.

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Equality in Education

I am in favour of building a society in which all children have equal access to an education that meets their particular needs. But this does not mean that all of those needs are the same.

Having basically taken myself out of a public educational system that I feared wasn’t meeting my academic needs, and having put my children in special parts of the public system and/or at least temporarily relied on private services and facilities, I am well aware of the extent to which the availability of such options unlevels the playing field and gives unfair advantage to people like me and my children compared to those whose parents lack the interest or resources to optimize the education of their children. I am uncomfortable with that reality and would prefer a system where all children were provided with optimal resources.

But children are people with different interests and capacities, and although they all need to learn to socialize appropriately with others different from themselves, they also need acknowledgement and support of the areas in which they differ.

So I am not in support of the current efforts in many places to eliminate all “streaming” and special interest programs in the public school system (as described here).

The solution as I see it is to enrich the early years enough so that every child can discover special interests and make access to specialized programs as free as possible from economic and social barriers. And then every child’s education should receive an equal share of the total funding (except for exceptional cases of “special needs”), but that doesn’t mean that every child’s share of the funding should be spent in the same way.

Source: Vancouver Wants to End Classroom Inequality. But What about Mini Schools? | The Tyee

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Transcribing Speech of the Oppressed

I was actually a bit creeped out by the excessively phonetic transcription in this harrowing account that was reproduced by Cheryl Brown in Quora’s ‘Black History & Politics’ section. Commenter Linda Keres Carter shared this feeling and started an interesting thread of back and forth on the issue of how much phonetic transcription is appropriate.

To me it’s not so much a matter of the ‘dem’s and ‘dere’s being obtuse as disrespectful. There is a fine line between using phonetic transcription to create genuine atmosphere and sympathy and using it for mockery (of which there has been a long tradition). In the 1930′s, even sympathetic recorders (such as the one quoted by Cheryl) often quoted with a level of attempted phonetic “realism” sufficient to raise the suspicion of condescension and at least the enablement of outright mockery.

PS Cheryl (the OP) responded quite positively to Linda’s suggestion.

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The Hostage Exchange is welcome (and overdue)

Of course, as the CBC reports 

The timing of the releases of Meng, and Spavor and Kovrig, show China clearly saw a connection between the two, several diplomats and foreign policy experts told CBC News.

“China … up until now, has said that there’s been no linkage between the two, but by putting them on the plane [Friday night], they’ve clearly acknowledged that this was hostage-taking,” said Colin Robertson, a former Canadian diplomat for more than 30 years.

But China’s claim of no linkage has always been a joke. Not in the sense of a naive but incredible claim of innocence, but rather as a deliberate mockery of the corresponding claim by Canada and the US.

That Meng was a hostage being taken as a bargaining chip was clearly implied by Donald Trump’s comments early in the game, and in some cruel sense China was right to respond with tit-for-tat (perhaps deliberately being more obvious about it while maintaining the ridiculous posture of denial). And to my mind, the only Canadian politician or diplomat with any dignity in all this is John McCallum who pointed out (just shortly after I did) that the extradition request was obviously tainted. This is especially sad given that cabinet actually had the power to legally override the treaty “obligation” without waiting for any judicial approval.

Perhaps it is time to add that the “justice” system in the US is no longer sufficiently credible to justify any continued extradition treaty at all, as it is riddled with prosecutorial malpractice including but not restricted to the use of plea bargains to extract tainted evidence and the extraction of false confessions by bullying and mental torture  (Central Park Five, Aaron Swartz)  and also their selective use, abuse and denial of the extradition process (Assange, Sacoolas).

Canada’s behaviour as a sycophantic slave to US demands is rightly seen by China as an indication that our claim to independent nationality following the “rule of law” is as much a farce as China’s claim that the Michaels were fairly convicted as spies.


Source: Michael Kovrig and Michael Spavor arrive in Canada after nearly 3-year detention in China | CBC News

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Why doesn’t philosophy progress from debate to consensus? | Aeon Essays

Source: Why doesn’t philosophy progress from debate to consensus? | Aeon Essays

My first thought on this article was to be puzzled by the idea that Molyneux problem is not trivial. Surely any person handling and feeling a sphere will notice the continuous symmetry of that experience relative to rotations of position relative to the object whereas that of handling the cube is only discrete (one feels edges and corners at different positions depending on one’s orientation relative to the cube). And similarly. the visual experience of thesphere is the same from all directions but that of the cube is not. So why would anyone not immediately make the correct identification on first seeing and comparing the objects?(but see third comment below!!)
My thought on progress in philosophy is that once a question becomes sufficiently well defined for consensus to be possible it becomes, by definition, a question of what we now call science. What is now called ‘Philosophy’ thus remains the domain where we try to come to grips with what is really meant by questions posed in the languages that we inherit from our almost pre-human ancestors with words like “should” and “good” and “why” which often express a mix of feelings that may vary from person to person and tribe to tribe.
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The world can learn from South Africa’s ideal of nonracial democracy | Aeon Essays

Challenging perspectives (|and contrary comments) on a deeply painful situation that provides a reflects our own – albeit in a strongly distorting mirror.

Source: The world can learn from South Africa’s ideal of nonracial democracy | Aeon Essays

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(239) If two more particles bond together to make a bigger particle, what happens to their wave functions? – Quora

The quantum state of a system of two particles is represented by a vector in the tensor product of their individual sate spaces.This is made up of linear combinations of products of state vectors (including integrals as well as finite sums), and if the individual states are represented in terms of (say) position observables by functions \psi_1(x_1) and \psi_2(x_2) , then a general state for the composite system is a function \psi(x_1,x_2) where the special case in which \psi(x_1,x_2)=\psi_1(x_1)\psi_2(x_2)

Source: (239) If two more particles bond together to make a bigger particle, what happens to their wave functions? – Quora

The quantum state of a system of two particles is represented by a vector in the tensor product of their individual sate spaces.

This is made up of linear combinations of products of state vectors (including integrals as well as finite sums), and if the individual states are represented in terms of (say) position observables by functions \psi_1(x_1) and \psi_2(x_2) , then a general state for the composite system is a function \psi(x_1,x_2) where the special case in which \psi(x_1,x_2)=\psi_1(x_1)\psi_2(x_2) corresponds to two separately identifiable particles.

If there is no interaction between the particles then this product form of a “pure tensor” is preserved by the time evolution of the system, but if there is an interaction term in the Hamiltonian then the evolution may carry such a pure tensor into a linear combination (or integral superposition) in which \psi(x_1,x_2) is more conveniently represented in a form like \psi(x_1,x_2)=\psi_{cm}(x_{cm})\psi_{rel}(x_{rel}) where x_{cm} and x_{rel} are the coordinates of the centre of mass and of the internal coordinates describing the relative positions of the two particles.

\psi_{cm}(x_{cm}) is then the wave function of the new composite particle and \psi_{rel}(x_{rel}) is the internal wave function which determines its possible energy levels etc.

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My words may have meaning, your parrot’s may too.

A recent essay by Stephen Law in Psyche Ideas, entitled My words have meaning, your parrot’s do not. Wittgenstein explains, is forcing me into yet another diatribe in my ongoing love-hate relationship with “philosophy”.

A slogan often associated with the later philosophy of Ludwig Wittgenstein (1889-1951) is ‘meaning is use’. Here’s what Wittgenstein actually says:

For a large class of cases of the employment of the word ‘meaning’ – though not for all – this word can be explained in this way: the meaning of a word is its use in the language.

In order to appreciate the philosophical significance of this remark, let’s begin by looking at one of the key things that Wittgenstein is warning us against.

Suppose I say: ‘It’s hot today.’ So does a parrot. Saying the words is a process; for example, it can be done quickly or slowly.

However, unlike the parrot, I don’t just say something: I mean something.

OK. First I would say that the most important “philosophical significance” of W’s remark is not its content but its qualification “though not for all”. Would that philosophers were all so careful!

But by what right does Law say that the parrot’s utterance has no meaning?

And in that sentence, what is the meaning of “meaning”?

Suppose a parrot has been trained to squawk something that sounds vaguely like “It’s hot today” whenever the temperature exceeds 30C and “It’s cold today” when the temperature goes below 15C. Who is to say that the parrot doesn’t have some mental state which corresponds to a sensation of the temperature and prompts the appropriate response?

But even if it doesn’t – or if the parrot is replaced by a thermostat which triggers play of a recording of the appropriate sentence – the words still convey meaning to the listener.

Of course although the thermostat means something to me when it says “It’s hot today”, I think we can safely presume that it doesn’t mean something to itself. So if we interpret “I mean something” as meaning I have the intention of conveying information to another conscious entity, then perhaps when the parrot’s squawks “It’s hot today” it can be said to have no more meaning than when I make the same exclamation to myself when suffering the heat alone. But there is definitely a sense in which I do “mean” something by such an exclamation.

And with regard to the parrot’s capacity for “intent” I would suggest something like the following experiment:

Assuming that parrots are fearful of both cats and snakes but have different ways of responding to them, train a group of parrots to see a human associate the appropriate word with each kind of threat and then separately to copy a human saying the words “cat” and “snake”,  and then observe whether or not a parrot will imitate the human word in order to alert its mate or friend.

It may not work. But I can see no “philosophical” argument why it must be impossible.

Unless, of course, the parrot is dead.

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Plastic Peril

From strangled seabirds to trapped turtles to the giant floating island and the discovery of nano-particles in the flesh of the fish we eat, we are all aware of the horrors of widely distributed plastic waste, and so it is only right that we refrain from the use of plastic bags and wrappings – at least so long as there is not an effective system of collection and consolidation of such waste. But I take issue with some of the ways this is interpreted.

As I learned from the latest (May 30) issue of The Village Green, an Australian group called the Minderoo Foundation has produced a report which names and shames the companies responsible for plastic pollution. But I am surprised by their emphasis on “the base of the supply chain that make ‘polymers’ – the building blocks of all plastics – almost exclusively from fossil fuels.”

The GHG emissions attributed to plastics by Zheng&Suh in a letter at Nature Climate Change(cited as a reference by Mindaroo) are mostly from the energy used in their production, and from the assumption that they will end life in incinerators (which are the same for all kinds of polymer source, since plant based polymers could otherwise serve as a Carbon sink if not used for plastics and then burned).

But a proper energy transition (which is essential in any case) should resolve the former, and the current practice of burning waste is certainly not what I would recommend as the most climate-friendly alternative. In fact, collecting and burying plastic waste seems to me to be a potentially significant means of carbon sequestration. So, contrary to many who expound on this topic, I would suggest that what we need to do is not reduce our use of plastics but rather increase it – with the proviso that all plastic waste be separated and stored in a secure burial place (such as may be provided, for example, by fossil carbon extraction – eg old coal mines and oil wells).

Please let me know if you see anything wrong in the above analysis.

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The Village Green

My friend John Butler is back in fine form churning out issues of his wonderful newsletter on a regular basis.

His latest issue is a blockbuster – full of interesting, and sometimes challenging, content.

It starts with an account of local efforts to encourage pollinators in the Grey-Bruce area, but the ideas are relevant anywhere.

Next is news of a petition by the Ontario Clean Air Alliance calling for an end to gas-fired power plants in the province.

According to the Alliance, greenhouse gas pollution from Ontario’s gas-fired power plants will
increase by more than 300% by 2030, and by 500% or more by 2040 as the province uses gas
to replace aging nuclear plants and to meet growing demand for electricity from population
growth and increased electrification for electric cars and home heating.

And, yes, the emphasis was added by me to highlight my own pet peeve with those who claim that CO2 reduction is our absolutely primary concern while ruling out a possible solution without any serious attempt to weigh the relative risks.

Among other news, the same issue includes a report about the efforts at Squamish in BC to use electricity to produce fuel. In this instance it is by CO2 capture and reformation to produce a traditional hydrocarbon fuel (with the same net zero overall GHG effect as production of pure Hydrogen, but perhaps quicker adoptability into existing engines and systems). If this becomes economic – as eventually it must if we are to stop burning mined fuels – then it will place a huge demand on our electricity generation capacity, making full use of anything we can generate from (dare I say?) Site C, as well as any other non GHG sources such as wind, solar, and (dare I say?) nuclear.

And the article on ‘Assisted Colonization’ opens a huge can of worms. Not to mention the question of how we are more likely to assist species we find cute rather than ugly (or otherwise undesirable – I can’t wait for the campaign to “save the killer bees” when they are found to be being forced northward by excess temperatures in their previous homeland).

But we’re not even halfway through John’s latest issue yet!

There’s also an interesting set of reports about environmental progress in the Roman Catholic hierarchy (despite some blowback) to implement ideas expressed in pope Francis’ 2015 Laudato Si encyclical; and some less encouraging news from the Amazon with the slightly reassuring caveat that, with a better political will, “Brazil and other countries could become green superpowers, harnessing the Amazon’s natural wealth to export everything from sustainably cultivated cocoa, açai and fish to promising new inputs for cosmetics and pharmaceuticals”.

An extended discussion of a recent report from the Minderoo Foundation on plastic waste is something (like the nukes issue) about which I may have a rather contrarian position – but I’ll address that in a separate post.

Next comes a warning about the cyber-vulnerability of “smart” electrical power networks – which is something that we have just recently seen also applies to “dumb” hydrocarbon pipelines (though it’s hard to take too much comfort in the fact that the old world is just as vulnerable on that score as the new).

There is also much more in depth info about the big recent climate victories against Exxon and Shell, and a summary of the new Canada-Ontario Agreement on Great Lakes Water Quality and Ecosystem Health.

And then at last we get to the deep stuff!

In an essay on THE BANALITY OF CLIMATE EVIL John reinvestigates the question “Where does evil lie?”

Referencing Hannah Arendt and quoting a recent essay from something called the Centre for Contemplation and Action he draws parallels between the Eichmann of the holocaust and the corporate boardrooms of today.

The C4C&A essay quote ends with “As both Thomas Aquinas and C. S. Lewis taught, for evil to succeed, it must disguise itself as good, which is apparently much easier to do than we imagine.” I can’t resist noting that there is a delicious irony created in my mind between that sentiment and the famous line from American theoretical physicist and Nobel laureate, Steven Weinberg who once said, “With or without religiongood people can behave well and bad people can do evil; but for good people to do evil – that takes religion.” But leaving that aside, we are left with the dilemma of whether to accuse those who resist CO2 reduction of personal evil, or just of the error of having been confounded by the illusion of a purportedly greater good.

John takes this on directly with the following paragraph:

I have no quarrel with climate activists who choose to see “correct-incorrect” rather than “good-evil.” I understand that narrow moralization can burn people at the stake, figuratively and literally. Yet I believe in the importance of bearing witness to evil. I also believe that a reluctance to see or point to evil can lead one to become an impotent bystander at the edge of the unspeakable. I believe we need to make the unspeakable spoken

But he acknowledges “the risk of becoming the cult of the climate righteous” and quotes John Wesley, who put it well as a warning in his 1749 ‘A Plain Account of the People called Methodists’, where he expressed fear of “a narrowness of spirit, a party-zeal, a being straitened in our own bowels; that miserable bigotry which makes many so unready to believe that there is any work of God but among themselves.”

In the end John finds wisdom in an updated version of the old precept “Hate the sin but love the sinner” while acknowledging how difficult this often is to do.

And there’s more!

Many inspiring and relevant quotes and a selection of poetry round out each issue. Often we get a sample of John’s own verse but this time it’s a classic haiku and Victoria Sackville-West’s poem ‘Moonlight’.

In case you didn’t click on the link above, here’s another chance to check it out.

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What About a Truly Progressive Wealth Gain Tax?

The idea of a minuscule 1% Wealth tax has been promoted recently, but what I think would be better is a truly progressive tax on all wealth gains regardless of source – whether it be through employment income, capital gains, or gifts and inheritances.

What reasonable objection can there be to a tax regime which says you can keep 1/n of the nth $million of whatever wealth you gain, by any means whatsoever, in any given year?

This would mean (since 1/1=1) that there would be no tax at all on the first million dollars of income.

The second million would be taxed at a rate of 50%

The third at 67%.

And so on.

So an income of $2million (either from employment, capital gains, or inheritance) would yield an after-tax gain of $1000000+$500000=$1500000 for an effective tax rate of 25%

$3million would yield  $1500000+$333333=$1833333 for an effective tax rate of 39%

$4million would yield  $1833333+$250000=$2083333 for a net rate of 48%

And an income of $ten million (either from employment, capital gains, or inheritance) would yield an after-tax gain of

$1000000+$500000+$333333+…  …..+$111111+$100000=$2,930,000

for an effective tax rate of 71%.

And, yes, the marginal tax rate would be unlimited, so an inheritance of $1billion, if paid all at once, would have a marginal tax rate (on the last million) of 99.9% but the amount the poor exploited child would get to keep would still be almost $7.5 million.

But if the transfer was spread out over several years the tax impact would be a lot less – which might perhaps provide a useful incentive for effective succession planning!

The revenue (and taxpayer impact) of such a system could easily be adjusted by just changing the tax-free amount and step size from a million dollars to some other amount (such as, say, $100k)

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What is Murder?

It’s in the last minute and a half of this video that the doctor testifying in Chauvin’s defense provides what I consider the most damning evidence for the prosecution. It relates to the difference between the last two videos in my earlier post where, in the color negative version of the Floyd incident, the person who died was immediately placed in a recovery position and subjected to CPR.

It is never possible to really prove the intended outcome of an action, so I guess the legal definition of murder is generally more along the lines of an intended act (or omission?) whose consequence is known to almost certainly be death. In Chauvin’s case we can be reasonably certain that he knew of the possible risk of knee-on-neck restraint, but in my opinion it is not obvious that while Floyd was complaining Chauvin had any good reason to know that what he was doing was almost certain to cause death(*); and since it is often used by police, taking that level of risk is at least sometimes considered not to be murderous even if death does ensue.

But I think we can be almost certain (eg from senior police testimony) that Chauvin knew from his training at least that when Floyd stopped complaining, cardiac arrest was likely to have occurred (albeit very likely largely due to the drugs and panic as much or more than actual airway obstruction). And from that moment on, any interference with prompt attempts at resuscitation does amount to murder.

*- Perhaps it should be more widely known by police that knee-on-neck restraint is very likely to cause death when applied to people in a state of drug-induced panic – to the extent that using it at all in such cases should be prohibited, and should result in an almost automatic conviction for at least manslaughter if death does ensue.

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Coleridge’s Theory of Ideas

Well, I have to admit that I had been completely unaware of Coleridge as a philosopher until coming upon this Aeon Essay. But on reading it  I found much to like about what seems to have been his approach.

In particular I was impressed by the assertion that “seeing polarised debates as revealing an interdependent whole, he tried to embrace the views of his philosophical opponents, rather than simply dismiss them.” If true this would be a refreshing deviation from the impression I often got from reading philosophy that each new school was arguing against a wilfully over-literal interpretation of whatever its predecessor had tried to express in the probably always inadequate words and sentences of human language. Perhaps his poet’s ear gave him a greater understanding of the weakness of propositional language than seems to have been common among those who try to define perfect grand philosophical systems (often with the same effectiveness as the famous blind men studying an elephant without an understanding of the difference between “has” and “is”).

And I also like many aspects of how his ‘polar philosophy’ deals with subjective and objective ideas and how he seems to have thought of the age-old stress between thinking of parts and wholes (the many vs the one) as related to different mental functions (which some might now, perhaps too simplistically, identify with left and right brain hemispheres).

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Where does our “Number Sense” come from?

Source: Why do humans have numbers: are they cultural or innate? | Aeon Essays

The fact that we can reliably count to 152 and distinguish it from 153 does not mean that we have a “sense” of either of those numbers. In fact I know of no-one who does. But they are not “social constructions” for us either.

Our understanding of the distinct features of 152, while not directly built into our brains, is an inevitable consequence of certain simpler features that are built in  – namely the tendency to clump aspects of our experience together into distinct objects (including the finding of smaller clumps within larger ones and conversely identifying groups of clumps as new bigger clumps), to identify pairs or groups of clumps as being somehow the “same” as one another in various ways (eg as having equivalent elements, as having the same small number of elements, or as having similar structure in space or time, or…), to have some idea of “relationships” between different things with the possibility that a putative such relationship may be “true” or “false”, and to have rules of “logic” that allow us to relate the truth and falsehood of various such relationships. Any entity with these capacities, even if alone in the universe, might well learn to distinguish 152 from 153, to factor both of them, to recognize 151 as prime, and even to prove Fermat’s Theorem and wonder about the Riemann Hypothesis. There is definitely nothing social or cultural about any of that (apart from the names with which we label the various concepts).

Of course that doesn’t make it all a “real” feature of the universe (though I guess it would be real by definition as a feature of our minds if those minds were really capable of implementing it to all levels), as it depends on those inherited means of processing data which may or may not suffice to describe and predict things at all levels of accuracy.

This is basically just a rehash (or messed up complication) of what I said last time, but the second half of Ball’s article brings up another important point.

Although the arithmetic of large numbers can be analyzed in terms of mental tools which only include built in models for very small ones, we do have (and share with other animals) other ways of dealing with quantity. These involve intuition about relative magnitudes which allow us to compare them without the use of discrete numbers. These comparisons often seem based on geometry (and sometimes fail us – especially as children – when the physical scales conflict with the quantities we are asked to compare). They also often seem based on ratios, and so involve a logarithmic relationship to the additive scales we sometimes use for the same quantities (perhaps also related to the physiological structure of some of our sensory apparati).

Whatever the reason, I think it is important to recognize that our built-in mental apparatus for recognizing and comparing quantities may have (at least) two completely distinct components, which may have evolved to meet different environmental pressures, and may be located in different parts of the brain with different types of implementation. A deeper understanding of this may well be extremely useful in mathematics education, and also perhaps in many other situations where quantitative information needs to be communicated to a wide variety of human types.


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Are Numbers “Real”?

This Aeon Essay about whether numbers are cultural or innate is a rerun from 2017. But I read it again and it strikes me that the claims attributed to cognitive scientist Rafael Núñez are wrong on at least two counts.

Yet whether numbers really exist independently of humans ‘is not a scientific debate, but a philosophical, theological or ideological one’, said Núñez. ‘The claim that, say, five is a prime number independently of humans is not scientifically testable. Such facts are matters of beliefs or faith, and we can have conversations and debates about them but we cannot do science with them.’

This is doubly wrong.

First, I would argue that whether numbers “really exist” independently of humans is indeed a scientific question with little to learn from philosophical, theological or ideological perspectives.

And secondly I would say that, if numbers “really exist”, then the fact that five is a prime number independently of humans is indeed scientifically testable.

But first things first. The question of whether numbers “really exist” is really a question about whether or not our propensity to identify parts of our experience as separate countable things, and the binary logic that we use to relate propositions about them, are in fact capable of providing an optimal means for making predictions about what we will experience – or whether some modified “quantum” logic about not-exactly-countable objects with fuzzy boundaries may eventually do a better job. (Yes, some Philosopher may tell me that’s just one “Ontological Perspective”, but I would just ask them to come back when they have a better one.)

And with respect to the primality of five, I would say that (so long as our conventional rules of logic survive the test of experiment) one kind of scientific test of a proposition is provided by showing its logical relationship to others that have already been established. And the primality of five is indeed a logical consequence of the basic properties of numbers that we already consider well tested. (And, yes, some Philosopher may tell me that’s just one “Epistemological Perspective”, but I would just ask them to come back when they have a better one.)

But the article does raise some interesting questions about how our capacity for inventing and/or understanding numbers evolved – which I think are worthy of a subsequent posting.

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The Problem with “Scientism” is the Word

This is old enough that I may have already responded to it. And after more than half a century maybe I should admit defeat. But every time I see that word I re-live the indignation I felt as a 17 year old being forced to sit through a course on ‘Scientism, Man, and Religion’ and not being able to focus on anything other than the outrageous etymological dishonesty of introducing that pejorative term with the effect (obviously intended because any literate scholar would see it) of causing confusion in the public mind between the mental attitudes of a scientist (which is what the structure of the word implies) and an uncritical devotion to science as our only source of truth and value (which would have been better referred to as “scienceism”).

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