If you’ve followed the career of Simon Conway Morris, the famous Cambridge paleontologist, you’ll know about his work on the Burgess Shale as well as his refutation of Stephen Jay Gould’s thesis that the animals in that formation represented fundamentally novel phyla that died out due solely to “historical contingency.”
You might also know that Conway Morris is a devout Christian, and has bent some of his science toward natural theology: the use of natural history to give evidence for God and understand His ways. So, for example, Conway Morris’s 2003 book Life’s Solution: Inevitable Humans in a Lonely Universe, a discussion and list of “convergent evolution” (lineages of animals or plants that, though unrelated, come to resemble each other), was part of a Templeton-funded project whose underlying theme was that the uniqueness of human intelligence was the result of God’s intervention.
Conway Morris, then, seems to be drinking the Kool-Aid of religion, co-opting his science in service of praising and giving evidence for God and Jesus (who are, of course, One Being). That is certainly the lesson from Conway Morris’s new scholarly paper in Studies in History and Philosophy of Biological and Biomedical Sciences (free download, reference and link below), which makes no bones about adducing “evidence” for God from mathematics.
Try reading it yourself. It’s a long and tedious read, made harder by Conway Morris’s penchant for what he thinks is breezy and readable prose, which in fact he has no idea how to produce. The article is loaded to the gunwales with phrases that Conway Morris thinks are clever, but in fact weigh down his prose and distract from his thesis. Here are just two examples:
For example, if the minimum additional weight that needs to be added to eighty ounces (or if you prefer 2268 g) for me to perceive a tangible difference is one ounce (for those of you wedded to Gallic certainty that is of course is 28.35 g). . .
and
Be that as it may, and with no reason to doubt that our mathematics would not emerge without some sort of cultural foundation, is our competence in this regard any better explained? In this context, I am rather wickedly reminded of the plot situation familiar to the less able writer whereby the narrative has ensured that the hero is trapped in some impossible predicament (chained in steadily flooding cellar, that sort of thing) until the author picks up the pen and continues “ and with a mighty bound he was free”. So in an analogous way lurking at the back of the numerosity debated that is to ask how on earth the numerical approximations employed by animals like a rhesus monkey or guppy can be squared with the capacity to employ square roots (let alone complex numbers), there nestles an all-purpose and perhaps too convenient explanation.
Oy! That is just bad writing, and the paper would have been immensely improved had Conway Morris not been so infatuated with his own cleverness.
But I digress. Here, as best I can make it out, is Conway Morris’s argument:
- Some species of animals show “numerosity”, that is, they can distinguish between greater or lesser numbers, as in crows distinguishing between three pieces of food and five.
- But ONLY HUMANS can “count” and do abstract mathematics (find square roots, solve equations, etc.) To Conway Morris, these unique abilities depend critically on human consciousness and language.
- The mathematics we engage in is not just a human invention, but is in fact the discovery of mathematical truths that are independent of human devising. When we do math, we are discovering already-existing truths that are “out there.” (I believe this view is called “mathematical realism”.) As Conway Morris says, “mathematics inhabits a transcendental world.” And here we begin engaging with the numinous.
- We have no idea how humans actually do math: it doesn’t seem like something that would arise naturally from our evolution. As Conway Morris says,
. . . claims for an evolutionary basis for a capacity for abstraction seem to rest on weak ground. This emphatically is not to contest that we at least require neuronal equipment and such a nervous system could only arise by the processes of evolution. It is, however, to protest that we are not a whit closer to explaining how even relatively simple mathematical operations are actually conducted. Related to this is the sense that effective mathematics is impossible without language and in this sense is a test-case for consciousness itself.
Here he gets even closer to the idea that doing math is something that reflects a gift from God. If you think I’m exaggerating, Conway Morris quotes Robert Kanigel on the remarkable mathematical gifts of Srinivasa Ramanujan, well known to many. The bit below is longish, but I think is necessary to quote in full, as it suggests that Ramanujan’s abilities had a divine source (Kanigel’s quote, my emphasis):
“It is uncanny how often otherwise dogged rationalists have, over the years, turned to the language of the shaman and the priest to convey something of Ramanujan’s gifts.. [R]epeatedly [mathematicians] have been reduced to inchoate expressions of wonder and awe in the face of his powers, have stumbled about, groping for words, in trying to convey the mystery of Ramanujan.. [I]n the language of the Polish émigré mathematician Mark Kac, [Ramanujan] was a “magician,” rather than an “ordinary genius.” Mystery, magic, and dark, hidden workings inaccessible to ordinary thought; it is these that Ramanujan’s work invariably conjures up, a sense of reason butting hard up against its limits.
But at reason’s limits does something else take over? Do we here flirt with spiritual or supernatural forces outside our understanding? T. K. Rajogopolan, a former accountant general of Madras, would tell of Ramanujan’s insistence that after seeing in dreams the drops of blood that, according to tradition, heralded the presence of the god Narasimha, the male consort of the goddess Namagiri, “scrolls containing the most complicated mathematics used to unfold before his eyes.”
Of this Conway Morris says two telling things:
Such a view is, of course, congruent with the view that mathematics inhabits a transcendental world. As Morris Kline (1980, 323) notes there are individuals and schools that “affirm that the mathematical concepts and properties exist in some objective sense and that they can be apprehended by human minds.”
and
Ramanujan’s encounters with his god ring very true, but I may be engaged in wishful thinking.
Now the first bit is just adumbration of mathematical realism, but the second claims that our ability to apprehend those “out-there” truths may come not from naturally selected brains, but from God. And that this is in fact Conway Morris’s view is clear from his last paragraph (my emphasis).
There is another observation, linked to this thought. Oddly the idea of animal numerosity being extrapolated to human mathematics almost always presupposes that our neural architecture actually has any capacity to know the world. This, however, may not be true unless we have an independent warrant that tells us that what we believe to be true is in reality truly true. Darwin saw the abyss and dithered, unable to take the plunge. It is, of course another story, but such a warrant exists. Not on the basis of unreflective faith, the recurrent gibe offered from Huxley to Dawkins, but because in a world of radical uncertainty we have only two options. One is to erect a thanatocratic culture, of existentialist despair, where suicide rates grow and euthanasia is “legal”. The other is to become creatures of trust. Curiously enough, and from a very different direction, in his essay “Sorry, but your soul just died” Tom Wolfe (2000, 109) comes to what I think is a similar conclusion. Speaking of our existentialist morass that Nietzsche so presciently identified, Wolfe writes of “modern man plunging headlong back into the primordial ooze. He’s floundering, sloshing about, gulping for air, frantically treading ooze, when he feels something huge and smooth swim beneath him and boost him up, like some almighty dolphin. He can’t see it, but he’s much impressed. He names it God”. Back to square one.
The first bit is straight out of Alvin Plantinga’s playbook: natural selection could not possibly have given us the ability to apprehend truths about the cosmos because natural selection favors not apprehension of truth, but ability to survive and reproduce.
I’ve criticized this view in Faith versus Fact, and of course the answer is simple: in many (but not all) cases, natural selection could give us the ability to apprehend truth and the tools (rationality and logic) to do it, because apprehending truth helps us to survive and reproduce. (If we can’t tell a lion from an antelope, we are in big trouble). Sometimes, of course, we don’t apprehend truth: optical illusions and other false beliefs (i.e., we’re smarter than most other people) could also be the results of natural selection, but a form that promotes false beliefs because they can be adaptive, too.
At any rate, at the end of the paragraph Conway Morris goes off the rails, claiming that “in a world of uncertainty” we must choose between nonbelief in God, leading to nihilism and despair, or to become “creatures of trust”, i.e., believers in God. Can there be any doubt from the above that this is what Conway Morris means?
Finally, his notion that disbelief in God leads to nihilism is refuted by simple observation: most atheists haven’t taken to their beds in despair, nor wallow in sorrow and gloom. And euthanasia and suicide—really?
Here’s the last bit of his argument:
- Our ability to do math, one aspect of our ability to perceive what is real, is a gift from God.
The purpose of the whole piece, if you can slog through the prose, is to show that the “unreasonable effectiveness of mathematics” is evidence for God, so that science buttresses Conway Morris’s Christianity. Now THAT sounds like a Templeton project, for Sir John Templeton’s belief—and the goal of his bequest to his Foundation—was that science, studied properly, would support the existence of God.
It’s no surprise, then, that you find this at the end of Conway Morris’s paper:
TEMPLETON again! But that’s not surprising: the organization has supported Conway Morris for years. In fact, I’ll venture a guess here: Conway Morris, who’s rapidly becoming the Francis Collins of paleontology, will win the million-pound Templeton Prize within five years.
Below is a video of Conway Morris attacking materialism as an explanation of consciousness; it’s more or less a plumping for dualism. He’s presenting a God-of-the-gaps argument based on the puzzle of consciousness. This is the kind of stuff that Templeton loves: in our ignorance resides the divine. Note that he at 4:29 he regards the Resurrection of Jesus as true, because it’s simply impossible to make up that kind of story!
I’m still amazed that a scientist as good as Conway Morris can accept the reality of the Resurrection on evidence so thin that he’d never use such a line of reasoning in his scientific work on fossils!
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Conway Morris, S. 2016. It all adds up. . . Or does it? Numbers, mathematics, and purpose. Studies in History and Philosophy of Biological and Biomedical Sciences. Online, http://dx.doi.org/10.1016/j.shpsc.2015.12.011
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If my ability to do maths is a gift, I’d like to return it for something else because it sucks.
Yep, if mathematical ability were a “gift from God” then how come many people dislike maths and are pretty bad at it?
Ability at maths doesn’t come easily, we need to formally train children extensively over large parts of their childhood in order to make them any good at it.
And even then, only a fraction will get as far as complex numbers and similar things mentioned by Collins.
This is not evidence for any gift from God (unless God is being remarkably stingy), it is evidence of a brain being deliberately re-purposed with quite a lot of struggle.
Only a fraction will get as far as fractions.
It’s a SIGN that they’re for the furnace.
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Did God keep the receipt?
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And Common Core is a gift from Lucifer …
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Sometimes only “Oy” will do.
“Yo! Y? Ω.”
“Oy…”
And then they come back around to “there are only X alternatives”, blah blah blah.
No, probably not. There are probably more than two alternatives.
I suggest that Conway Morris propose the mechanism by which his dualistic thingy that supposedly does the truthing pulls the strings in the brain.
That is just incoherent. For natural selection to improve survival, it mus (and can only) deal in truth about the world. True within the required tolerance.
Evolution wouldn’t work on propositional content, like “true” and “false.” If it did then babies would inherit their parents’ beliefs. We don’t sense truth content — we sense representations. And would an entirely misleading system of representation be adaptive?
Evolution isn’t working with truth or even accuracy: it works for reliability. And it only has to be reliable enough — ‘within the required tolerance,’ as you say.
I think correctly apprehending the world about one fits with most people’s idea of “truth”. You need a true (enough) grasp of what’s really there to survive.
The fact that common sense often gives wrong answers to very large and very small physics questions doesn’t negate this, in my opinion. Newton was right; but just not on every scale. And it was hard to improve on his very accurate estimate of physics.
An nice example of how evolution selects for truth:
“A certain kind of beetle mates with a certain kind of Australian beer bottle”
http://www.livescience.com/16331-discoverers-beetle-beer-bottle-sex.html
Evolution tries us to keep safe enough to reproduce, that’s all the truth about reality we normally need.
If humans where selected for truth there would be no religion; not many heated discussions about evolution; we would never lie, there would be no racism etc…
And science would be much easier 🙂
But of course the human race has been subject to the much faster cultural selection for centuries, now. Which is good news and bad news; the good being that it can proceed much more quickly; we need only agree its the proper course…
There is certainly a lot of change,
but personally I don’t see much progress in cultural evolution. I believe utility and convenience usually win over truth.
Nevertheless, if we keep on trying to implement things like Universal Human Rights, we still can be optimistic about the future.
“…but personally I don’t see much progress in cultural evolution.”
I hear ya!
“…natural selection favors not apprehension of truth, but ability to survive and reproduce.”
Of course, one then has to ask why apprehension of truth and an ability to survive/reproduce are exclusive of each other.
For goodness sake!
I can’t believe someone so intelligent is still using the argument, “We haven’t worked it out yet, so it must be God.”
This has been proven wrong over and over again as our understanding of our world progresses.
As for the Jesus resurrection story being true because you just can’t make that stuff up, that means he must also accept the resurrection stories of the faiths that came before Christianity. Or does he take the Bill O’Reilly track – Christianity is different because it’s true?
The quoted excerpts of Conway Morris reveal a masterpiece of muddled thinking. Of course I think Jerry makes more sense, but the problem I am just starting to grapple with is that I need to know more about why Jerry makes more sense! I’m working on it, but not there yet.
I don’t know where to begin.
I guess “bullshit” will do.
One of the most interesting non-subject courses I took in grad school was an engineering lab course that took the students from producing simple conducting wires up to stop watches and other basic circuits. And while I don’t remember much of it, I remember that combining standard transistors into specific patterns can duplicate pretty much any basic mathematical and symbolic logic operation you want. All you need for a human to do math is neurons with an input, output, and gate hooked up together in the right configuration, or a ‘software’ equivalent thereof.
This is interesting, and would go toward explaining the abilities of savants to solve problems without seeming to consciously think about them. They could have neural circuits that work something like how a calculator works, and they are able to tap into it.
I vaguely recall reading that savants likely have brain architecture anomalies that bring certain functional parts closer together than normal. this enhances certain associations.
A simple example is the condition in which people associate colors with numbers – color synesthesia. I had a case of this when young. I remember 3 was green, 6 was always blue, 7 was red, etc. I have since lost this ability. I think the condition is fairly common though.
Savants, I think, have something similar which speeds up some kinds of numeric processing.
Which soundly refutes the idea that “only humans” can do math. Unless one wants to posit that computers have souls.
All math can be derived from a basic truth table; that’s how all of our computers do math (true/false of a truth table represented as 1/0). You pretty much learn this in compsci 101.
After reading the mush of Mr Conway the only course is to file it under ‘forgettable’.
So Conway Morris thinks 1+1+1=1 and he thinks math proves god. Go figure.
1+1+1=1 but only for small values of 1.
🙂
And 2+2=5, for sufficiently large values of 2.
(This actually works in an Excel spreadsheet, if the column format is set to zero decimal places and you type in 2.4 plus 2.4…)
cr
I once worked on a CORAL 66 compiler which evaluated (or rather, generated code to evaluate) 2.0 / 2.0 as -1 … and this was in fact the correct answer! Something to do with fixed-point arithmetic and overflow into the sign bit on a 16-bit processor, I recall.
If the values are zero.
1+1+1=1 If we are talking about Boolean algebra this is of course True
There’s an argument that a lot of our conscious thinking is heavily dependent on our unconscious thinking – and a lot of this unconscious thinking is metaphoric and affected by the sensations in our bodies. Affection is Warmth, Morality is Purity, Happy is UP, Sad is Down. Indeed George Lakoff and Rafael Nez published “Where Mathematics Comes From” to argue at great length that higher mathematics is also grounded in the body and embodied metaphorical thought.
So there is one alternative (whether it is true or not) right away. The human body and brain together form a moist analogue computer which can handle mathematics as a by-product of ‘computing’ to survive.
It would also seem to me that a living species with a complete inability to recognize and deal with patterns — or a universe with a complete lack of patterns or indeed any regularities at all — would be very, very difficult to design. Impossible, maybe. We’d need a God to explain that.
Fortunately that’s not the sort of universe we find ourselves in.
Morris seems to believe that if there are two trees in the forest, neither one can be higher than the other one unless there is a Mind to do the measuring and counting.
Bishop Berkeley: “Esse est percipi” ~ to be is to be perceived and therefore God does the perceiving of the natural world for it to have an existence. No one says who perceives God though.
Plato lives! But Plato’s weird and wonderful arguments are nowhere to be found.
Also, although practicing mathematicians are often (they *say*) mathematical realists, as far as I can tell most philosophers of mathematics are not. Some mathematicians regard that as unfortunate. However, if one carefully analyzes some of the “peripheral remarks” of some mathematicians, the distinction becomes harder to draw. For example, Dedekind seems to have been a factionalist and Brouwer was an intuitionist (which is compatible with both realism and not; I am not entirely sure which he should count as).
The view known as “structuralism” is also popular, though I think this is a way to skirt the metaphysical (rather than the epistemological) questions, sometimes.
Oh WTF, Morris … please do grow up.
There are just so many points of confusion here it’s hard to know where to start. First he introduces a completely unnecessary radical skepticism because animals do not evolve to discern propositions. And then he drags in the old “we can’t handle the truth” THIS sorry state of affairs would lead to, if truly believed in…. Oo, scary.
Followed up of course by equivocating on the word “trust.” Gee, if we trust reason and trust our senses, isn’t that just like trusting our Mommy and Daddy? Phase 3:
PROFITGOD!!!11!1“We stand today at a crossroads: One path leads to despair and utter hopelessness. The other leads to total extinction.
Let us hope we have the wisdom to make the right choice.” (Woody Allen)
Our minds are able to recognize similarities which provides the basis for a concept. A specific number is a concept and the relevant similarity in this case is that each particular member subsumed by the concept can be put in a one to one correspondence with every other member. The concept can then be represented by a word, for example, the word TWO names the concept whose members comprise all duos. There’s nothing transcendental going on here just an extension of how our minds evolved to keep us alive. Distinguishing a lion from an antelope rests on our minds ability to recognize similarities and upon encountering new instances of an animal accurately determining to which class (concept) it belongs.
Impossible to make up stuff like the resurrection? My kids could make up more believable stories.
Only children could believe his nonsense. Religious belief is the best example we have of adults maintaining childlike ideas despite reason and evidence.
It’s the old ‘because my mind boggles therefore God’. Some people should try harder.
“Impossible to make up stuff like the resurrection?” I think he’s picked up this argument from prominent British apologist/philosopher NT Wright:- the resurrection is so implausible that it must be true (does he not know of the origins of scientology, mormonism, islam etc). I find it dispiriting that great minds (albeit with a narrow focus) can be so easily deluded.
I’ve heard the “must be because couldn’t have been made up” so many times for so many competing claims of similar character (usually religion, but sometimes cryptozoology, ufology, etc.) it isn’t funny. Do these people ever compare notes …?
So galling that some people actually make money by just making things up.
There were 304,912 new titles and re-editions produced in the U.S. in 2013(Wikipedia). I suspect the vast majority are made up stuff.
OK, good reply. 🙂
A moldy stew warmed over, growing more distasteful for every time.
The short answer is that mathematics is a tool, but so is a hammer. No one takes a hammer to a nail and says “therefore magic!” There is a lot of math that was less useful, even wrong and/or unfinished [ https://en.wikipedia.org/wiki/Calculus ], so the ones that need to put glimmer on it has to cherrypick.
Since we now know plants can count, does that mean math somehow becomes more special? [ http://www.bbc.com/news/science-environment-35371349 ] And for that matter, even atoms can count. [ https://en.wikipedia.org/wiki/Energy_level ]
From special the magic believers deduct magic. “Mathematical realism”, is that what people call platonist dualist magic these days? Unfortunately it is a rare type of magic that can’t be tested for rejection, fortunately it is a rare type of magic that can’t be tested for rejection and extraordinary claims need extraordinary evidence.
For spice, Morris adds consciousness, a function of the body, and gifted individuals – but aagain has to cherrypick [ https://en.wikipedia.org/wiki/Savant_syndrome ] – and claim we don’t know everything yet. Well, I guess we don’t, therefore science. A scientist like Morris should know better.
Is’nt Mr Morris, a palaeontologist, wading a bit far out of the depths of his scientific expertise here? Has he even bothered to check with neuroscientists, cognitive scientists and other experts whether his ‘thinking’ actually comports with their best current understandings of these topics? Or is he just like many other cranks – blundering into topics he knows little about fully believing his expertise in palaeontology automatically translates to expertise in other disciplines as well?
Mathematics is nothing but applied logic, and the ability to logically deduce an accurate conclusion from a premise is highly adaptive. The amazing scope of modern mathematics is just the sum of billions of instances of this mechanism in action. Tellingly, humans weren’t running around the savannahs of Africa doing abstract mathematics in their heads (if they were, the earliest records of written mathematics would be much more sophisticated). It’s only when we get civilization, language, and leisure that something akin to what can be called mathematics as we recognize it today emerges.
Moreover, I think there is plenty of current evidence to suggest that some crows, robins, and cormorants can all “count” in some way, not just distinguish between greater and lesser amounts of something. And when was it established that we are the only species capable of doing basic algebra? If a parent crow returns to the nest with food for one of two chicks, does it know that it must make one additional trip before it sees the begging gape of the second chick? I don’t know, but I don’t think anyone else does either at this point.
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One divided by a newly-hatched chicken? It is with shame that I admit I require an explanation.
An additional trip per chick!
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D’oh. Don’t know how I missed the connection to Ed’s comment.
You weren’t the only one.
I often think my d*g Maggie knows some geometry. At least she finds her way in the woods as if she was laying down a fairly accurate geometric pattern in her brain for later reference.
I once saw fairly conclusive evidence that my parents’ cat understood geometry.
The cat was sitting on the window-sill in the living room of my parents’ home, when a large rooster (recently acquired by a neighbour) walked across the grass in front of the window, to the utter fascination of the cat. He watched the rooster until it walked around the corner of the building and was out of sight – then he jumped down, ran into another room and jumped up onto the window-sill there, so that he could see the bird again.
So he clearly understood that although the bird was no longer in line of sight from one point, it would in the line of sight from another point!
Yes, logic + counting. That’s it.
A very telling video. I’d like to know why he finds the idea of the resurrection so novel. He sounds wishy-washy, like there might be some personal relationships he’s trying to protect. Hey, that kept Darwin from publishing for 20 years!
And the Jesus story isn’t the first resurrection story, not by a long shot. Why doesn’t he believe in those earlier ones? Afterall, they’ve been around longer!
I had one (well, several actually) Xian tell me that Xianity must be correct: It’s psychologically impossible that so many millions could believe it for so long without it being true.
(After suppressing the urge to say, “get out much? Read any history, ever?”) I asked him why he wasn’t a Hindu, if his reasoning was based on durability? Hinduism has been around much longer.
If the ability to do Mathematics came from a god (issues of Theodicy aside), it would seem like a pretty big deal, setting us aside from most animals, who either don’t, or choose not to, do math. Wouldn’t a god say, “Behold, you can do math!” Yet, not even the Book of Numbers, which would seem a likely place to look, touts this gift.
+1
The Book of Numbers contains lots of columns of figures with an incorrect total at the bottom. Presumably when God gave us the ability to do maths*, he lost the ability to do it himself.
*It is a plural as it is an abbreviation of mathematics.
Don’t forget arithmetics. 🙂
A Reading from the Book of Armaments, Chapter 4, Verses 16 to 20:
Then did he raise on high the Holy Hand Grenade of Antioch, saying, “Bless this, O Lord, that with it thou mayst blow thine enemies to tiny bits, in thy mercy.” And the people did rejoice and did feast upon the lambs and toads and tree-sloths and fruit-bats and orangutans and breakfast cereals … Now did the Lord say, “First thou pullest the Holy Pin. Then thou must count to three. Three shall be the number of the counting and the number of the counting shall be three. Four shalt thou not count, neither shalt thou count two, excepting that thou then proceedeth to three. Five is right out. Once the number three, being the number of the counting, be reached, then lobbest thou the Holy Hand Grenade in the direction of thine foe, who, being naughty in my sight, shall snuff it.”
A basic treatise on ordinal numbers, I think.
Good thing that the ordinal number for the Holy Hand Grenade isn’t, say, omega. 🙂
Actually, at a very (very very) basic level, we do have evidence—in fact, a spoken report—of a non-human animal displaying comprehension of numbers beyond merely comparing more and fewer: Alex, the famous parrot, could count. (Though not very high!)
Alex could also do addition, at least if the problem summed to eight* or less.
http://blogs.nature.com/news/2012/02/alex-the-parrots-last-experiment-shows-his-mathematical-genius.html
*I think. I could be misremembering the limit.
“The mathematics we engage in is not just a human invention, but is in fact the discovery of mathematical truths that are independent of human devising.”
Math is a collection of descriptions and definitions. When we engage in math we draw conclusions based on the implications some definitions or descriptions will have for other definitions or descriptions. You may as well claim the English language dictionary would exist without the need for humans to create it. The definition of “zebra” does not exist independently of humans; zebras do. The Pythagorean theorem doesn’t exist independently of humans; the triangles it describes do (or at least could, albeit imperfectly).
Good point.
And the ‘magic’ ingredient is that algebra can’t be deduced from logic, but can be broken down into axioms that people can agree on. (Or sometimes not, if they want to go further than the rest. Say, constructivists.)
It is a game, a very useful one at times mind.
But if games were measures of efficiency and magic, playing Tic-Tac-Toe is the Kalam argument of math.
I thought Russell and Whitehead sort of said algebra could be broken down into logic and vice versa. Algebra being part of Maths.
Thanks, Torbjörn.
I think what rickflick is getting at just above is that (and it is not without trepidation that I, a musician, presume to pronounce on math to a physicist), while logic may not produce the axioms, how one proceeds from the axioms must be a form of logic. No?
In a way. But that the rules cannot be codified completely and consistently and usable in every case. So it is a more semantic notion – or such is the claim – than a proof-like one.
(This is complicated.)
The distinction between a breezy day and a windy day is small, but the distinction between breezy prose and windy prose is very great.
There are certainly more elegant statements of the same thesis about. (Michio Kaku comes to mind.)
While a non-believer may find ALL such arguments motivate them to reach for a coffee (and want to suggest to the writer that they need to smell the coffee), Morris in addition makes one require an aspirin!!
Mr Conway Morris as a paleontologist should be able to recall Richard Owen’s assertion that the human hippocampus minor made us different from the apes and therefore a creation of God.
Mr Conway Morris seems to have blundered down a similar dead end, this is not good, this is the result of dogma.
If my memory isn’t totally shot, I believe I recently read the the Venus Fly Trap uses rudimentary counting when deciding if that fly in its grasp really is a meal
I saw that too. On the first tap, nothing. On the second it snaps shut. With further struggle, it exudes digestive juices. You can see how such an ability to “count” would be adaptive.
I leaned something of this first hand when I fed my carnivorous plant pets years ago.
You fed pets to your carnivorous plant? Man, that must have been some big plant! What was it, a triffid? @)
Don’t know the species, but it was a very strange flytrap sold by a Chinese man.
For Dog’s sake don’t feed it after midnight!
And stop watering it!
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“Don’t know the species, but it was a very strange flytrap sold by a Chinese man.”
…who called it Audrey.
What sorts of pets did you feed your carnivorous plants? 😉
Always refresh before posting.
Atoms seem able to work out some pretty cool geometry. Carbon secures atoms around it at ~ 90 degree angles. Other atoms assemble atoms around them again at mysteriously precise angles according to laws of geometry.
Atoms are smarter than a 3rd grader!
A notion that I think about sometimes is that in different lineages there can be some ability that gets pushed by directional selection, and if extended enough an emergent ability starts to appear that was not clearly there in the simpler forms.
For example, lots of animals can do rudimentary echolocation, but in some lineages like bats this has been pushed to where they can build pretty detailed mental images out of sound.
Fish can sense electrical field and the electrical fields of animals around them, and many can weakly manipulate that field. Many fish use this to navigate and communicate, but it is so powerfully developed in electric eels that it is a powerful weapon.
Directional selection for better problem solving skills in primate societies leads to ‘insight learning’ (chimps for example show flashes of problem solving abilities that seem genius compared to other apes). One can clearly see that extending these problem solving skills above that of an ape is an advantage. Our brains seem more like the result of an evolutionary arms race with other species, and of course with our own species. Notice how in our fossil record that as new kinds of humans appeared with bigger brains and better tools that the earlier kinds of humans later disappeared.
There is a position, not widely known and often very naively misunderstood, which would easily show Conway’s assertions to be nonsense (which I think they are). Yet this position certainly accepts the existence of abstract objects, which here would go by the name ‘mathematical structures’. It is rather simple, but subtle, and does agree in many ways with Platonism and with mathematical realism, but goes far beyond them. And it certainly shows much deeper appreciation, of what mathematics appears so far to be, than, e.g. the simplistic ‘just a tool, like a hammer’, which needs no further discussion. And finally, it obviously solves the often stated conundrum (“unreasonable effectiveness of mathematics in basic science”, a matter which is more sophisticated than many misunderstandings one hears), the conundrum of why mathematical discoveries of structures, such as complex separable Hilbert space, and of differential manifolds, can much later turn out to be exactly what fundamental physics needs.
This position is just that nothing exists except mathematical structures. And they all do. Full stop. The so-called physical universe as we know it is (at least part of) a mathematical structure, one which physicists have groped for at least since Newton, and one which no one can be sure exists (Weinberg’s “…Final Theory”, to quote part of one of his books’ titles). This position is often called the MUH (guess the expansion!) of Max Tegmark, who is a cosmologist, not a philosopher. No refutation, nor claim that he is unoriginal here, has been close to success, to my mind. Especially given Sean Carroll’s advocacy of the Everettian form (some mistakenly say ‘interpretation’) of Quantum Mechanics (i.e. just plain QM with no measurement problem, but a surprising-to-many-of-us assertion of Many Worlds), I would be very interested to know his thoughts on this (and those of other physicists here of course).
I don’t regard myself as qualified to assert MUH’s truth, if that can even be verifiable in any reasonable way. But refutations so far don’t convince me at all, even the few from scientists who have actually read Tegmark’s papers on it (just go to his MIT website to find them).
In particular, any crow or raccoon, one who knows anything about ‘our’ physical universe, and they know plenty, is doing mathematics in using their partial knowledge of that abstract structure. I’m just waiting for someone to again assert that the world cannot actually be abstract, apparently shown by comparing our fates after he descends from Jerry’s apartment on the elevator and I jump out the window. But don’t expect a reply.
Tegmark’s hypothesis is odd, to say the least, not the least of which is that it is unclear what the scope of the thesis is: how many cumulative hierarchies are there? (And how does one answer this?) And that’s *just* more or less conventional set theories. The mathematical universe is not well defined, it seems to me.
(Disclosure: I’m a fictionalist about mathematics.)
I agree, Keith, that the MUH hypothesis is more than one hypothesis, because the notion of “mathematical structure” is certainly non-unique. But I don’t think this non-uniqueness makes it meaningless in the extreme way that so many assertions whose verification is completely impossible are utterly meaningless.
Note also that Tegmark himself has ‘backed off to the computable’, so to speak.
Might one not wonder whether perhaps the mathematics of quantum field theory, in particular the standard model for particle physics, is non-unique in the same way? I don’t know enough to get anywhere with that. But if the answer is yes, I don’t think your “odd” is quite the right word as a criticism.
I also don’t think your use of that word “odd” is in the direction of the following, so this following is not disagreement with you: But surely Special Relativity’s non-reality of observer independent time, all sorts of bizarre seeming consequences of quantum theory, and so on, even maybe Newton’s ideas originally, and Maxwell’s fields, would all have been considered very odd to most scientists initially. So “odd” in that conventional sense would be more a complement than a slam when referring to fundamental science. I’d say the same for the Everett (so-called) interpretation of QM.
But if Tegmark or anyone else (and he used to) claim ‘all’ structures, he has to tell us what that means exactly. IOW, if he’s restricting to one “cumulative hierarchy”, why? Why is the universe not category theoretic? Why ZFC (for example?) and not some other set theory?
By contrast, if you use mathematics as the *tool* it is in ordinary physics, then you can use whatever you want, because it has no ontological implications at all (in the same way). Bunge has a good theory of reference which shows this clearly (if complicatedly).
“Odd” was my polite way of saying: “Platonism, really??” 🙂
As a professional mathematician, let me assure you that most humans are really terrible at mathematics, and even the best mathematicians aren’t that great. After all, we still haven’t been able to prove the Riemann hypothesis or prove P != NP.
So much for Conway Morris’s argument.
In my limited experience (as an engineer), I see that most people struggle mightily with simple multiplication and especially division. Algebra? fugettaboutit.
But, as someone who has with disturbing regularity committed the “factor of 2 error” (forgetting to multiply or divide by 2 where appropriate in a given engineering problem), I can’t really talk about it …
And don’t forget the “off-by-one” category of errors in programming!
Early on in my career I had to drill into myself the axiom that the number of elements in an array is “high bound minus low bound PLUS ONE”.
sub
Isn’t being a Bible-believer really the nihilistic option?
One is compelled to love a god who gave Adam and Eve the death penalty because they were naive: They were created so innocent that they had no reason to imagine that a talking snake would steer anyone wrong. And BOOM! A long-fuse death penalty for every living thin for all time. THAT is a nihilistic god!
Jesus does not redeem this horror, both because he is one and the same as the terror-god, and because he repeatedly mocks and condemns those who try most sincerely to follow all the rules he set down as the terror-god. One gets the sense from the test of the Bible that if you truly love Jesus, he will despise you and call you a hypocrite. Again, nihilistic!
The best a believer can hope for, then, is post-mortem unity with a terror-god who has unleashed a plan that requires beastly suffering for all living things.
Wow. Reading those excerpts of Conway Morris’s prose is like tearing through the packaging of an air-mail delivery to find a trinket within.
There’s a trinket?
It seems to me that the same arguments can be made about any human ability – music for instance. Just as there are mathematical geniuses there are musical geniuses. There are people with extraordinary abilities in every human field of endeavour. Just because an indian mathematician had psychotic dreams doesn’t make mathematical ability, his or anyone else’s, divine in (its) nature.
In any case the foundation of mathematics are sets of axioms which are completely defined by humans. By choosing the axioms we want we can actually create mathematical systems that seem to have nothing to do with reality
Not sure about the dying out of novel phyla during the Cambrian, but something tells me that, had Gould lived to see it, Conway Morris’s religiously motivated, Templeton-funded reinterpretation of the Burgess shale might’ve put the kibosh on Gould’s assertion of NOMA.
“For example, if the minimum additional weight that needs to be added to eighty ounces (or if you prefer 2268 g) for me to perceive a tangible difference is one ounce (for those of you wedded to Gallic certainty that is of course is 28.35 g). . .”
Oh dear, that’s really a bit like what the Deepak does – use a bunch of technicalities to try and sound profound. Damn mathematical showoffs, give ’em an inch (25.4mm) and they’ll take a mile (63360 inches, 1.609344km).
(And I’m sorry to say I didn’t even have to look those up. Guess I must be God?)
cr
Hang on, if he’s going to use the beliefs of Ramanujan to bolster his case, how can he claim that this provides evidence of the Christian god, and not of the goddess Namagiri (and by extension the rest of the Hindu pantheon)? Isn’t that a bit parochial?
If anyone has access to Hofstadter’s “Godel, Escher and Bach”, there is a 4-5 page discussion on this (562-566).
Hofstadter mentions that, despite Ramanujan’s genius, he does occasional make incorrect hypotheses, so the “God-given” theory needs to address this.
Also his friend G.H.Hardy, an eminent mathematician himself, was asked (after Ramanujan’s early death) whether he believed there was any occult or “exotically flavoured” elements to R’s thinking, to which Hardy replied that although he couldn’t answer with confidence or conviction, he didn’t believe it.
A rather more open-minded take that Prof. Conway Morris’s, IMO.
“I’m still amazed that a scientist as good as Conway Morris can accept the reality of the Resurrection on evidence so thin that he’d never use such a line of reasoning in his scientific work on fossils!”
+1
And I’d like him to tell us why he chose Christianity as his religion, and not one of thousands other religions out there. Did he study other religions, did he evaluate their miracles and truth claims and found them to be less trustworthy or downright false? Was his decision-making process true to his scientific profession in the slightest? Or did he just pick the religion of his parents/tribe?
The mathematics we do obviously aids to our survival. So natural selection can favor it.
That we also do mathematics, which has no obvious link to survival, can be explained by cultural evolution.
More God-of-the-gaps: I (and a lot of other people) can’t explain this phenomenon, so God did it.
I haven’t read the paper, so I’m relying on Jerry’s synopsis.
If we take “count” somewhat narrowly, to mean the use of number-symbols (like “five”), then it may be true that only humans can do it. (But I don’t think we should completely rule out the possibility that some animals could be trained to do it, or might even do it naturally.)
That depends on what you mean. It can be taken in a completely naturalistic/materialistic sense, but I suspect Conway Morris is taking it in a Platonistic/supernatural sense. In the naturalistic sense, what of it? The fact that the Earth orbits the Sun was an “already-existing truth” before humans discovered it. Why shouldn’t humans be able to discover already-existing truths?
Some of us have an idea, at least enough to dispel the sense of mystery. When trying to understand these things, it’s usually best to start with the simplest cases, and imagine a gradual progression to more complex ones. So let’s start with counting. And suppose we have a child who has not yet learned to count (use number-symbols) at all. It’s not too difficult to understand that the child can be taught to say the sequence of words/symbols “one”, “two”, “three”, etc, by rote. She can also be taught to associate those words with a sequence of ordered objects, such as fingers. And she can be taught to associate them with successive-sized groups of objects: one apple, two apples, three apples, etc. This can be further developed by encouraging her to explicitly count the number of apples in each group, e.g. “one…two…three”, for the group of three. None of this seems particularly mysterious. But it explains our most basic mathematical ability, counting. Of course, there are prior complex cognitive skills that are needed for these tasks, such as the ability to recognise discrete objects. But these are not specific to mathematics. (By the way, I’m not saying that children generally learn counting skills in quite such a structured way as this. I’m giving a simplified description.) Given those skills, and other language skills that are not specifically mathematical, it shouldn’t be difficult to see how even a child can have the ability to state such “already-existing truths” as “there are two other numbers [integers] between 4 and 7”.
“In this context, I am rather wickedly reminded of the plot situation familiar to the less able writer whereby the narrative has ensured that the hero is trapped in some impossible predicament (chained in steadily flooding cellar, that sort of thing) until the author picks up the pen and continues “ and with a mighty bound he was free”.”
Isn’t he missing a rather obvious chance to use the phrase “Deus Ex Machina” at this point?
That is, after all, pretty much his entire argument.
“Note that he at 4:29 he regards the Resurrection of Jesus as true, because it’s simply impossible to make up that kind of story!”
Firstly, in fact it is so impossible that the pagans invented that story multiple times centuries before the Christians stole it.
https://en.wikipedia.org/wiki/Miraculous_births
http://www.liberalamerica.org/2015/03/17/5-near-identical-jesus-christ-myths-that-predate-jesus/
http://listverse.com/2009/04/13/10-christ-like-figures-who-pre-date-jesus/
The early Christian apologetic was that the pagans invented those stories to discredit the Christian version centuries later.(!!)
Does Morris also regard “Jack and The Beanstalk” (complete with a beanstalk reaching the clouds, golden egg laying goose and giant) true?
Secondly, Morris deftly demonstrates how religion lovingly embraces credulity and totally rejects critical reasoning and evidence. The result being so astonishingly stupid that it requires a huge “miracle” to even start to believe it. Among believers, the more absurd the greater the belief because it “must be true”.
If you take the idea of “make up a story” to mean – for the first time ever – then it is impossible for the same story to be “made up” more than once. It can only be borrowed or stolen, as you say, after the first creative event. In that sense, Morris is correct to say the story could not have been made up, since it had already been written down long prior to the Christian era. Give credit where credit is due – the Greeks or Egyptians or someone else has the copyright.