What is "Mind?"

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yanqui

climber
Balcarce, Argentina
Jun 27, 2017 - 10:27am PT
I'm posting again. I'm not evil. I'm just weak, like Homer Simpson.

Michael Harris with a few thoughts on the possibility that computers could become the mathematicians of the future:

http://www.slate.com/articles/health_and_science/science/2015/03/computers_proving_mathematical_theorems_how_artificial_intelligence_could.html

MH2: I think most mathematicians who are not working in foundations or who are not accustomed to thinking about these axioms in a formal way, would also find this characterization of the axiom of infinity a bit puzzling at first glance. On the other hand, the statement: There is a set of natural numbers, seems crystal clear. Mathematicians did plenty of interesting mathematics for at least 2500 years (Euclid wrote down some pretty cool stuff back in the day) before Cantor came along with sets and even then his ideas were not generally accepted at first. It was later on that mathematicians generally agreed to base their work on axioms using this language.

In theory (at least when we're not speaking categorically) mathematical proof should be reducible to axioms (like these) using formal logic, although such a formal description of the proof would probably be incomprehensible to most human beings. The language we use to talk about the things we study and even to write down proofs is much more perspicuous. Otherwise I doubt we would be able to think about and solve mathematical problems. However (outside of the realm of say, categories) this language should ultimately be definable in the language of sets. There are reasons, I think, we have agreed to this, if you'd like I could could say more. On the other hand, if you want to be a professional mathematician and publish papers in this day and age, you are pretty much forced into this agreement. I don't know any working mathematicians (except maybe category theorists, who get to do what they do anyways) that might feel limited in their work by this agreement.

In terms of these axioms, just remember: even in mathematics, nothing is written in stone!

Hope that helps.
jgill

Boulder climber
The high prairie of southern Colorado
Jun 27, 2017 - 11:12am PT
There are formal proofs of theorems, and these can be dry and uninspiring, a sequence of strange looking lemmas presented in preparation for a quick and systematic finale. This is a kind of AI approach to theorem proving, one that leaves the reader wondering how in the world someone dreamed that up?

I have been guilty of this back when I published papers, but in retrospect what I was doing was making it easy for a referee to validate my efforts, rather than showing the hidden artistry of discovery and creation. What is far more important IMO is a commentary describing the development of interesting ideas. These days a mere sketch of the proof suffices for me.

When you leave the environment of formal publishing and just play with ideas there is a sense of freedom, like solo climbing.

Set theory can be both beautiful and dreadful, a mathematical quicksand that most practitioners avoid - unless you work in those areas. The Axiom of Choice is a prime example of shaky ground.

If, in the future, AI produces theorems that human mathematicians can't comprehend, I suppose applications, also incomprehensible, would follow. We would be left to oil and polish the machines, a pyrrhic victory for mankind.
okay, whatever

climber
Jun 27, 2017 - 12:14pm PT
I like John Gill's last sentence, in particular.
yanqui

climber
Balcarce, Argentina
Jun 27, 2017 - 01:16pm PT
The Axiom of Choice is a prime example

Wary of the V-scale, crash pads and the Axiom of Choice. You're so old school, Mr. Gill!
Dingus Milktoast

Trad climber
Minister of Moderation, Fatcrackistan
Jun 27, 2017 - 01:48pm PT
Ward, your boxed quite incorrectly engages the term "hubris."

Impressive!

DMT

Jan

Mountain climber
Colorado & Nepal
Jun 27, 2017 - 01:51pm PT
Back to sexual selection and evolution.

Sexual selection operates at the individual level but also at the societal level depending on the forms of marriage. A polygynous society will magnify a man's genetic impact while a polyandrous one will magnify a woman's. Polygyny will select for older men with more wealth and discriminate against young ones who however attractive otherwise, never manage to marry and reproduce because they are not wealthy enough. Polyandry will select for women who have major diplomatic skills and prefer an active sexual life.

Monogamy features more opportunity for the masses to marry and reproduce - for better or worse. Late age of reproduction while helpful to individual careers, is not so good for the gene pool. Down's syndrome percentages rise alarmingly with the age of the mother and autism is now being correlated with the age of the parents, including the male. The cultural preferences of post industrial society along with our good medical care are definitely impacting evolution in rich societies and not for the better. Overall, monogamous marriage opportunities and their offspring are devastating the planet.

And then there's 1st cousin marriage, preferred by 1/3 of all societies in the past but genetically dangerous today in the era of modern medicine. While preserving family wealth it also results in higher rates of birth defects among those who practice it. In the past, these genetic mistakes which average about 25%, died.

Nowadays both Arabs and West Virginians who still practice cousin marriage and Amish who have mated among a small gene pool for 200 years now, are all suffering higher rates than normal. In West Virginia it's something like 3 1/2 the birth defects of other Americans while the Amish have such a high rate of rare and severe genetic diseases that it is speculated they will be 100% of the population in another hundred years or so, a self induced extinction if it continues on as currently. Inbreeding is also one of the major hypotheses for why Neanderthals became extinct.

Sexual selection matters to individuals but in evolution, it's the practices of populations, the bigger the better, that counts.







healyje

Trad climber
Portland, Oregon
Jun 27, 2017 - 02:02pm PT
Human females are not biologically monogamous - quite the contrary, so it says something about the power of social norms and culture that they, at least to appearances, can override / rein-in a strong biological imperative to the contrary.
MH2

Boulder climber
Andy Cairns
Jun 27, 2017 - 02:37pm PT
yangui wrote:


There are reasons, I think, we have agreed to this, if you'd like I could could say more.



You have been generous enough, already.


I have read other mathematicians who point out that what mathematicians call and rely upon as proofs include intuitive leaps that are not supported in the way that formal logic would call for.


It seems to work anyway, though, and I don't think Paramecium depends upon a rock-solid fundamental formal logical proof of its ability to survive, either.





edit:

And I learned a new word:


Perspicuous

adjective formal

1. (of an account or representation) clearly expressed and easily understood; lucid."it provides simpler and more perspicuous explanations than its rivals"


◦ (of a person) able to give an account or express an idea clearly.
 



Jan

Mountain climber
Colorado & Nepal
Jun 27, 2017 - 02:50pm PT
Stronger than the urge for sexual variety for most women, has been the instinct to provide the best possible circumstances for the survival of children. Recent surveys have found women prefer having affairs with very masculine looking men who are unconventional but choose men with softer features (less testosterone) and more stable situations to marry.
paul roehl

Boulder climber
california
Jun 27, 2017 - 03:00pm PT
Human females are not biologically monogamous - quite the contrary, so it says something about the power of social norms and culture that they, at least to appearances, can override / rein-in a strong biological imperative to the contrary.

Oh, oh... sounds like a metaphysical problem.
Ward Trotter

Trad climber
Jun 27, 2017 - 03:26pm PT
Ward, your boxed quite incorrectly engages the term "hubris." It would take a wall of text to explain. I put my dick on the table as far as all things literary. Like my marathon time of 2:55, no one on ST can touch me in terms of literature.

Sycorax-woman, you need to try your hand at scrumpy poetry:

some salty Norfolk samphire
cheddar cheese on toast
Cornish pasty with gravy
Melton Mowbray pie
A Kendal Mint cake
Scrumpy jug
Aye!

Scrumpy jug indeed!!

Aye?

Ed Hartouni

Trad climber
Livermore, CA
Jun 27, 2017 - 08:46pm PT
MH2

Boulder climber
Andy Cairns
Jun 27, 2017 - 09:07pm PT
Indeed.


But sometimes objective evidence is needed.



I did not realize that my mind had gone wondering and got lost until I found among papers in my room:



Credit: MH2



I have no idea where it came from.
Jim Brennan

Trad climber
Jun 27, 2017 - 09:16pm PT
Sully/Sycorax has left her dick on the table.

Who amongst us all, will take up the challenge ?

This is life as lived by the rules of Philosophy. Be brave and step forward.

jgill

Boulder climber
The high prairie of southern Colorado
Jun 27, 2017 - 09:53pm PT
Wouldn't want to touch that with a ten foot pole.

(She is such a flirt!)


;>\
Ward Trotter

Trad climber
Jun 28, 2017 - 03:10pm PT
I've been in a bad mood ever since the US lost the America's Cup-- and now this!

LOL
eeyonkee

Trad climber
Golden, CO
Jun 28, 2017 - 04:20pm PT
It occurs to me that those of us who believe that mind is simply a product of biological evolution on this earth really don't believe in "mind" other than as a more or less Platonic ideal. What biological evolution produces are organisms with minds. The plural is the key. Each has it's own history, if nothing else.
MH2

Boulder climber
Andy Cairns
Jun 28, 2017 - 04:59pm PT
Each has it's own history, if nothing else.



In memory of Ben Lexcen.



http://adb.anu.edu.au/biography/lexcen-benjamin-ben-14154
eeyonkee

Trad climber
Golden, CO
Jun 28, 2017 - 05:18pm PT
Okay, so back to sexual selection. Here's my current view. The predator-prey dynamic is probably largely responsible for setting up the whole "imaging of the other guy" apparatus in certain lines of mammalian evolution, including ours. It set the stage for the jump from imaging the other guy to imaging yourself in human evolution. Imaging yourself in the context of other humans is what humans can obviously do. It is evolved behavior, of course, and humans are, above all, social animals (well maybe not above the bees or the ants or the Borg).

Something that is not absolute but typical in mammals is for the females to be the selecting agent in the male-female relationship. It is true of humans, of course. I can see where intelligence might be selected for over and above good survival genes, particularly in times of plenty, where surviving isn't the main driver. Good looks and/or intelligence ("he makes me laugh") may be more important in these situations. My guess is that there are relatively long times of plenty followed by short, catastrophic times of decidedly not-plenty, where the pure-survival genes are more important (natural selection). Frankly, it's not much of a stretch.

It occurs to me that this is how it might work with females. Let's say that they have just two response algorithms; 1) go with the guy I am most attracted to or 2) go with the guy that is most likely to ensure the survival of me and my children. I can see how epigenetics could be employed to make the female adopt one or the other based purely on outside stimulus.
eeyonkee

Trad climber
Golden, CO
Jun 28, 2017 - 05:41pm PT
I didn't get it at first (because I'm a big dope), MH2. Way to transition poignantly.

Been here and gone.
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