# Living in Avalon

…If you assume any rate of improvement at all, then the games will become indistinguishable from reality….given that we’re on a trajectory to have games that are indistinguishable from reality and those games could be played on a set up box or a pc or whatever, and there would probably billions of such computers or set top boxes…it would seem to follow that the odds that we’re in base reality is one in billions…tell me what’s wrong with that argument.

When I saw him answer the simulation question, I was immediately reminded of  the 2001 film, Avalon.

The simulation question has been talked about extensively in the last month or so, but I still haven’t seen any physicists chime in and it seems an argument from this perspective would be most appropriate for Musk (1). There was a response from a cognitive scientist and a philosopher here, but they seem to have missed the mark a bit, and they don’t seem to have understood what Musk may have meant by indistinguishable. I’m going to focus on this word, because it makes specific demands on the physics of the possible technologies involved.

Questions:

1. Is it possible to build a simulation “indistinguishable from reality?” Indistinguishable is critical here.
2. I expect the trajectory Musk describes will change. Where is the asymptote? I will have no chance of answering this one.
3. If it is possible to build such a simulation, does it matter?

Re: Question 1: Is it possible to build a simulation “indistinguishable from reality?”

[All Equivalent] I am going to assume, as Musk seems to, that by “reality” he means a world that operates with the same rules as ours appears to; that it has the same laws of physics. The distinction he is making is between “base” reality and simulated reality. They both behave exactly the same but one is an original. His argument seems to require all of the simulated realities operate under the same rules, so that our experiences here can carry implications about what’s possible in realities that simulate other realities.

[Computable] I think I have to assume further, also like Musk, that “reality” is computable. That all of the rules can be reduced to logically rigorous statements, also that there is nothing that doesn’t follow the rules, and therefore classical or quantum computations are sufficient to simulate reality (2).

It happens that our experiences here operate under quantum mechanical principles at the most fundamental level. We live in a universe that obeys Heisenberg Uncertainty, and there is a fundamental scale set by a constant of nature:

$\Delta x \Delta p\ge \dfrac{\hbar} {2}$

Any object we observe has a momentum ‘$p$‘ we associate with what Newton called a “quantity of motion”, and a position ‘$x$‘. This inequality is an assertion about the distributions of position and momentum. Roughly speaking, the uncertainty principle sets an absolute, fundamental limit on how well it is possible to know $x$ and $p$. This limit comes from the quantity $h$ – it is Planck’s constant. It is an incredibly small number measured in units of space and time we’re familiar with, but it is not zero, meaning it is impossible to know both the position and momentum of an object perfectly.

The less obvious consequence for our purpose: the uncertainty principle represents the limits in nature’s own detail. Once you know as much as uncertainty principle permits, there really is nothing else to know: nature itself carries no more information (3).

It shouldn’t seem plausible that a full fidelity (“indistinguishable”) simulation of a physical space could be housed in any volume less than or equal to that space, but I don’t know how to prove this. My intuition says the most parsimonious way to simulate a  physical space is to have that volume time evolve on its own. As Einstein put it, “God does not care about our mathematical difficulties. He integrates empirically.” There shouldn’t be any shortcuts, I think.

Some work on the limits of computation using uncertainty principle, general relativity  (GR) (and/or?)  the second law of thermodynamics has been done, producing theoretical limits regarding computation. This work is bit out of my depth but it seems GR is required for its limits on energy density (4). Anyway, these details should not interfere with reaching this implication: Because there are fundamental limits on computational power, and by [All Equivalent] these limits apply to a simulating reality, it is not possible to embed, as a subsystem, an indistinguishable simulation of a region within that region. There can’t physically be any substitute for proper reality.

Now, what about the plug-in Matrix kind, aka the dream or the video game? Maybe it is only necessary to fully simulate observed, or observable regions of space and time? And even then only to the limits of observational powers of the individual. I have been assuming that our “reality” fully obeys all the known laws of physics, even when we don’t directly test or observe them. I should just be able to say this kind can be rejected because it is solipsism – we are trying to use physics here and this would take all the bets off. But I think I can do better, especially since it was this kind Musk directly proposed, though I will have to offer inductive arguments.

1. This world is too shitty for too many people. Unless Musk somehow thinks this reality is his very own oyster and none of the rest of us are real, what reason would we have to simulate a reality like this with so much suffering?
2. All software has bugs. “Indistinguishable” is too strong a demand for any software to meet with, no matter how advanced its developer. Honestly I think bug-free software cannot exist. There would be dejavu’s and glitches.
3. This reality is definitely not a video game in its lack of lucidity. Why don’t we know it’s a simulation?
4. If we had this kind of computational power, we could do a lot better for a video game than this. It would literally make gods out of everyone. Just ask: are you living in the world you wish existed?

If an indistinguishable reality were possible, it would not be desirable. The truth is too hard. If people had unlimited power to create their own realities they would hide from base “reality” in ways that are more robust and complete than religion and technology  allow them currently.

I have one remaining physical argument. We know that some physical systems are described by models whose equations lead to algorithms that are “hard” in this sense: That the computation time needed to predict observables scales so greatly that the computer would effectively require the lifetime of a universe in base reality to integrate, violating our [computable] assumption (5). This argument is not without a certain subtle problem.

Re: Question 2: I expect the trajectory Musk describes will change. Where is the asymptote?

I should just give up on this one for now…I suspect the bound found by Seth Lloyd is too generous but I don’t know how to improve it:

$\text{Max Operations Per Second}$ $\sim \dfrac{mc^2}{h}$

The numerator is the most recognized formula in physics: the rest energy of Lloyd’s “ultimate laptop” from relativity. Planck’s constant has appeared again because this is a quantum computer, and the computation speed is limited by how quickly one state can “rotate” into another state that is sufficiently …distinguishable, again determined by Heisenberg uncertainty(6).

Re: Question 3: If it is possible to build such a simulation, does it matter?

When we ask for indistinguishability we are asking, by definition, for a reality that will never fail to satisfy any demand we might make of it. It is impossible to devise an experiment that would reveal that it is a simulation. I don’t know why Musk is unsatisfied with this (7). Again by definition, these doubts would persist for anyone living in base “reality.”

I think a minimal plea for sanity requires us to take our reality as it presents itself. Further, that we take it as simply as it presents itself, and imagine no hidden variables, mechanisms, Wizards of Oz, Dungeon Masters, Cartesian Demons, or code beyond nature’s capacity for information, i.e. its ability to distinguish.

It is a hardcore, base reality that what can’t be observed really isn’t there. A simulated reality and a base reality if indistinguishable must be one and the same. Nature itself can brook no hypotheses about the unobservable. We cannot allow ourselves superstition, or even agnosticism if we are going to move past barriers of imagination. We’ll have to be atheist. Nature is just too creative and extends too far beyond our ken to allow us any less.

Maybe we should be hopeful that we are living in a simulation…either we develop simulations that are indistinguishable from reality or civilization ceases to exist.

Avalon, the legendary land
The isle of apple-trees and mist
Avalon is the land of elves
Where the hero comes today

Avalon, the legendary land
The hero set out there

Avalon is the land of elves
Avalon is the heavenly isle of shadows
Enchanted isle
The ship set out to an unknown voyage
Avalon…

1. There are reasons for a good physicist (not me) to stay out of this discussion. The primary one I’m thinking of being that this notion is, at least at face, untestable. Please take all of the physics presented here with a grain of salt.
2. One thing I’m definitely not sure of: would this reality simulation require a theory of everything, so that all of the physical laws would have to be known?
3. It might be argued that nature does know more, but simply behaves in a way that prevents us from knowing or observing any more. I think all hypotheses of this kind can be equated to a “hidden variables” description of quantum mechanics, and I believe all such theories have been excluded by Bell’s Theorem and its experimental verification(here, and here).
4. There’s a whole literature on this that I won’t be able to go into. I neglect distinctions  made between limits on memory capacity, the longevity of a record, and what research in this area may imply about time itself, and any relationships between gravity and thermodynamics. In due time, I think the research on quantum computing will reveal much more about these questions.
5. Most of the research in this area is for Classical computation – where the states of computer are strictly binary, 1 or 0. The situation for quantum complexity is less clear, as this field is still fairly new and many quantum algorithms are still being developed.
6. There is an energy and time relation analogous to the one for momentum and position, though its interpretation is a bit more subtle.
7. Really I think he didn’t mean the full quantum mechanical notion of indistinguishable, but I needed an excuse to write this post.

# There isn’t anything down there, you know.

In mathematics, you don’t get anything without making an assumption. Math doesn’t tell you what’s “true,” it only tells you what follows from the assumptions. It’s derivations are only as believable as the axioms that form the base of the structure.

The same is true about the whole of epistemology. In an earlier post I discussed the fractal that describes a person’s knowledge, and neglected any mention of its root. Well,

At root is pure assumption.

As Richard Feynman said once, “you have to allow something to be true.”(1) These things go down to the bone marrow of our worldview. I sometimes think that very often political discussions fail completely to sway anyone, like religious discussions, because we are never really getting to the root assumptions that people are basing their positions on.

I have invoked the “materialistic principle” here a number of times. Alternatively, one might assume object permanence(2), or the similar notion of conservation laws. Religious folks will take their texts, contradiction be damned.

But there is no safe ground. There is absolutely nothing that can be beyond doubt. There isn’t anything down there. William James(3):

Most of you are devoted for good or ill to the reflective life. Many of you are students of philosophy, and have already felt in your own persons the skepticism and unreality that too much grubbing in the abstract roots of things will breed….Too much questioning and too little active responsibility lead, almost as often as too much sensualism does, to the edge of the slope, at the bottom of which lie pessimism and the nightmare or suicidal view of life.

I don’t agree with James about the end result of this rooting around; he can only speak for himself. Sarte found existentialism down there, and in a way my own view is similar to his, though I am motivated by a desire to understand nature, and am not interested in hypotheses that separate human beings as agents that supersede nature’s principles or pretend them to be anything other than a consequence of same.

A choice must be made of where to “hook in” on the side of this epistemological mountain, and the choice must necessarily be arbitrary. I’m not sure anything can even be articulated without this. This entire post presupposes that the mind can examine itself in a rigorous way, and I’ve preloaded it with a lifetime of inferences.

A good part of my teenage years were spent rooting around and ruminating on largely useless questions like this, searching around in religious texts and philosophy for some sound basis (4). If you have not yet done this for yourself, I encourage you to take a few years off, with “too little active responsibility,” and engaging in “too much questioning.” It will be very enriching if you are the kind of person who survives staring into the abyss.

1. He was talking about magnets in that context. We don’t get to know why opposite charges attract and like charges repel…we must assume it. https://www.youtube.com/watch?v=MO0r930Sn_8
2. Try playing peekaboo with Ted Cruz. Enjoy this.
3. I am of course not a diest, but strongly urge anyone who hasn’t to read “Is life worth living?” William James is one of my favorites. https://archive.org/stream/islifeworthlivin00jameuoft#page/16/mode/2up
4. No, not even for morality will you find a sound basis. Common atheist claims of a rational basis for this ring false to me. For no good reason really, I just reject solipsism: I observe that there are what appear to be other people and creatures with thoughts, feelings and experiences of their own. I suffer and experience happiness and I therefore assume by their appearance that they too exist and so does their suffering. It satisfies me to alleviate even some small part of this suffering. Let this motivate my action.

# On Growth and Knowledge

Everybody has their favorite model of knowledge.This is mine:

The things we understand about the world are like the leaves on a tree. Every time we learn something, we have an opportunity to ask a question that goes deeper and further, bifurcating and allowing for new leaves.

Our knowledge expands like a fractal. There’s no limit to what can be learned because there is no limit to what can be asked. The direction that our curiosity tends to lead us creates our expertise, and where there is no curiosity there can be no growth.

I spent a long time wondering what it is that enables religiosity to persist, even among very well educated people. It is facile to suggest that religious people are simply stupid. It seems to me that it is better explained by the way people respond, not to what they know, but to the boundary between what they know and what they don’t: the outer edges of this tree, and the space of their ignorance beyond it.

How comfortable do we feel with what we don’t know? There’s no bound on the scope of possible knowledge – the more you know the more aware of your ignorance you become, because there should always be an exponentially increasing number of questions, assuming one has enough curiosity.

There is some basic, emotional response to this boundless expansion. Some people just need to feel like there is something or someone in control of that space, and that somehow they have access to that control through religious practices. There is a discomfort in that great, outer fog that apparently most of us would prefer to retreat from.

Notice another implication as well for the progress of science. The method of science can always get us the right answers, but we are the ones determining its direction. By their assumptions and their questions, scientists themselves can limit its range. There is no expectation that science can progress without a bias in its direction. This bias is best counteracted by diversity.

It is said that to be truly wise is to know that you know nothing. Hitchens once put it like this:

…the discussion about what is good, what is beautiful, what is noble, what is pure, what is true, could always go on.

Why is that important? Why would I like to do that? Because that’s the only conversation worth having. And whether it goes on or not after I die I don’t know but I do know it’s the conversation I want to have while I’m still alive.

Which means that to me the offer of certainty, the offer of complete security, the offer of an impermeable faith that can’t give way, is an offer of something not worth having.

I want to live my life taking the risk all the time that I don’t know anything like enough yet, that I haven’t understood enough, that I can’t know enough, that I’m always hungrily operating on the margins of a potentially great harvest of future knowledge and wisdom. I wouldn’t have it any other way.

And I’d urge you to look at those who tell you at your age that you’re dead till you believe as they do. What a terrible thing to be telling to children. And that you can only live by accepting an absolute authority. Don’t think of that as a gift, think  of it as a poisoned chalice. Push it aside however tempting it is, take the risk of thinking for yourself. Much more happiness, truth, beauty and wisdom will come to you that way.

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# Cogito, Ergo…

From Part IV of Descartes’ Meditations(1):

…as I then desired to give my attention solely to the search after truth, I thought that a procedure exactly the opposite was called for, and that I ought to reject as absolutely false all opinions in regard to which I could suppose the least ground for doubt, in order to ascertain whether after that there remained aught in my belief that was wholly indubitable. Accordingly, seeing that our senses sometimes deceive us, I was willing to suppose that there existed nothing really such as they presented to us; and because some men err in reasoning, and fall into paralogisms, even on the simplest matters of geometry, I, convinced that I was as open to error as any other, rejected as false all the reasonings I had hitherto taken for demonstrations; and finally, when I considered that the very same thoughts (presentations) which we experience when awake may also be experienced when we are asleep, while there is at that time not one of them true, I supposed that all the objects (presentations) that had ever entered into my mind when awake, had in them no more truth than the illusions of my dreams. But immediately upon this I observed that, whilst I thus wished to think that all was false, it was absolutely necessary that I, who thus thought, should be somewhat; and as I observed that this truth, I think, therefore I am (COGITO ERGO SUM), was so certain and of such evidence that no ground of doubt, however extravagant, could be alleged by the sceptics capable of shaking it, I concluded that I might, without scruple, accept it as the first principle of the philosophy of which I was in search.

In the next place, I attentively examined what I was and as I observed that I could suppose that I had no body, and that there was no world nor any place in which I might be; but that I could not therefore suppose that I was not; and that, on the contrary, from the very circumstance that I thought to doubt of the truth of other things, it most clearly and certainly followed that I was; while, on the other hand, if I had only ceased to think, although all the other objects which I had ever imagined had been in reality existent, I would have had no reason to believe that I existed; I thence concluded that I was a substance whose whole essence or nature consists only in thinking, and which, that it may exist, has need of no place, nor is dependent on any material thing; so that “I,” that is to say, the mind by which I am what I am, is wholly distinct from the body, and is even more easily known than the latter, and is such, that although the latter were not, it would still continue to be all that it is.

There is an error here (2). What is the “I”? What restrictions does the existence of thoughts and consciousness alone put on the forms it may take? Could the thinking thing really be independent of “any material thing”?

Let there be thinking thing, then. A mind. It perceives by some instruments, which correlate with the opening and closing of the eyes, the stopping of the ears. It exists with some temporal sense, such that it recollects “past” events, and anticipates “future” events. It sleeps, it dreams at different times, all correlated with changes in experience.

Clearly the mind doesn’t see without eyes. It doesn’t hear without ears. When the brain takes a whack, its function doesn’t continue independently and unaffected. There is clear physicality to experience, and there are a number of reasons to suspect the brain and the body are the substrates of the mind.

Let us assume, as I have done here before (the “Materialistic Principle”) that that which is not observable does not exist. It follows that the mind can only arise from what is physically observable about the brain (3, 4). I take it that the mind is not “hidden” somewhere inside the brain, then it follows that the mind is not an integral whole; it is an emergent property or process of the electrical signals that pass in and among the parts of the brain.

ASIDE:

Creatures are not made by design. They are evolved, but that process gives a striking appearance of design. It obvious that nature is capable of acting as if it was* a creative entity. Maybe not with foresight and planning, yet somehow with an apparent agency.

END ASIDE.

*It seems to me that we don’t grant nature the capacity to “truly” act creatively for this reason: We see too clearly the detailed mechanisms by which it achieves that appearance. There exists no integral whole for the mind as we trivially observed above; the creativity the mind possesses must also arise through a confluence of components, just as in the case of natural selection.

Clearly there is no god (5), and it would appear that nowhere(!) in the world is there a thinking, creating thing that does not arise from a confluence of more basic constituents in a distributed system. This system’s processes may be distributed more widely in time, as in the case of natural selection, or more tightly distributed in time but highly complex in space as in the case of the brain, but this consequence is unavoidable: selection is not “like” a creative entity, it is one in any sense we are willing to impart to ourselves.

You have heard of a “god of the gaps,” but there is a similar kind of error in reasoning when it is assumed – and it is assumed very commonly – that people posses free will. It is a kind of deification of the self; an intercession of a vague divinity, which, while totally normal and probably embedded as part of the adaptive process in humans(6), in this current discussion I posit that all agency is only apparent agency. Or equivalently, that that which is indistinguishable from agency is agency itself (7).

The development process in technology is so organic, especially for things in which researchers are taking advantage of the principles of evolution and adaptation. It seems strange to me that we should be so cavalier about allowing neural networks to train and evolve. These processes are so poorly understood (8), we risk putting ourselves in a situation where we will have created strong AI on accident before doing it on purpose, and not even knowing how we did it. As I have explicitly stated, the evolutionary process “has a mind of its own.” This cavalier attitude seems to stem in part from the basic assumption that we are so special, that we must be the only thinking things in the universe.

We are not so special, except maybe in terms of how rare a thing we might be, and maybe the processes that made us form an NP Hard problem, which therefore can’t be shortcutted, so that this planet really did necessarily invest a lot of time and sacrifice in creating our species.

But even if we are the rarer structure, we exist not so apart and different from the other structures of the universe. The differences of kind are not differences of kind solely, but come from differences of a quantity of pieces and a subtlety of their organization.

I recall the arguments of Lucretius and wonder why it should take so long for us to see that the types of arguments about objects and matter being made of atoms carry similar implications for our minds and the simplicity that underlies apparent complexity of all forms.

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1. From the translation at Gutenberg. https://www.gutenberg.org/files/59/59-h/59-h.htm
2. And I’m sure, somewhere in the reasoning I put forth to correct it, heheh.
3. Is the brain even separable from the body? Can I assume its function doesn’t distribute into processes occurring throughout the nervous system? I remember reading research articles about people’s emotional states being altered with the amputation of limbs, or after having artificial hearts implanted. If the brain relies so heavily on cues from the nervous system, it may not actually be able to access some states or engage in some processes without contingent parts. Or put it like this: Can a congenitally blind person imagine the experience of sight? Do you know what its like to be a bat? Can you even know what its like to reside in the body of another person? Even your identical twin?
4. Is the brain a quantum computer? What are the limits for what is physically measurable? I recall reading an argument in Schlausshauer that suggested it probably was not a quantum computer – or at least from what was known about neuron activity it couldn’t involve quantum mechanics. I’m just assuming that some microscale structure and electrical signals are as deep as you need to get for a brain.
5. This is a kind of implicit axiom on this blog, as a part of what I’ve been trying to do here is talk about things purely from a post-theistic worldview, i.e., what are the things we would think about if we were not chained to naive assumptions about the answers to basic questions and having to argue constantly with deists? I’ve thought maybe I should post more about the justification for atheism, but there doesn’t seem to be much point – I don’t dwell on it too much anymore, and it’s beat to death in the popular sphere.
6. Some lies it might be beneficial to believe, as I have mentioned on this blog before. I think this might be one of them. Apparently Isaac Singer said this: “We must believe in free will — we have no choice.
7. Notice the use of MP. There’s some real irony here. Some of these things I don’t think most people will realize until AFTER strong AI has been brought into the world and made them incredibly clear to everyone. If it satisfies the turing test, you have no choice: It thinks just as much and probably not too different from how you do.
8. I am suddenly reminded of the beautifully creative play of AlphaGo recently.

# A narrative of human evolution.

Scientists acknowledge, both male and female, that there is a serious problem of gender disparity in most of their fields. But there is an obstacle in getting the science community to truly understand the gravity of their gender problem, and I think even now in our “enlightened” age, many scientists still do not take the problem seriously. Men in science should be taking it personally, but they are not, and they therefore do not pursue solutions with the appropriate level of sincerity.

What most scientists do not understand – here I mean all genders – is that the science itself is suffering for the lack of women. In truth from a lack of diversity in general, but I want to use a specific example here which will highlight the gender problem.

It does seem to be a common perception, among those outside the community, as well as among many inside, that science is progressing in a largely unbiased way. The fact that we are necessarily approaching our questions from an anthropocentric worldview, though, seems perfectly clear. More important for the narrative here is that most scientists – in particular Darwin himself – are men. I am going to suggest that the prevailing narrative of human evolution is an male centered one, and this bias misses what might actually be the more important female half of the story:

The hair on most men’s arms is coarser and darker than that of boys, and it is not as fine as the hair most women retain into adulthood – this is called vellus hair. Vellus hair, then, is juvenile trait retained into adulthood, and it is more common for women to retain this trait than men. You will also note that this pattern does not occur among bonobos and common chimps. The evolutionary trend of retaining juvenile traits is known in biology as neoteny, and it has occurred for other species as well, and it seems to be associated with a pattern of domestication: dogs, cows, pigs, and cats have all undergone neotenous changes over the course of the last several thousand years. Vellus hair is a physical trait, like the diversity of fur colors which have appeared for dogs and cats, but it is not primarily the physical trait that is being selected for. Actually, it is a set of behavioral changes that are being selected – the physical traits are correlated with changes in behavior due to hormones.

It has been argued by some anthropologists that humans are self-domesticated apes(1). The implication of the changes described above being more pronounced in women is that the selective process has acted to a greater degree on them than men. This means the male-centeric idea of early hominids who stood up to use tools out on the savannah, and communicate amongst each other to better hunt prey is failing to account for half of the species obviously, but less obviously that the other half of the story may be the more important part!

Archeological finds within the last few years have shown it likely that humans were upright walkers prior to leaving the forests (2). This suggests the particular changes in brain development for humans are not solely associated with the opportunities of having the hands free, and ingenious new tool use. This was, and for many still is part of the standard Darwinian narrative. But if not tool use, what are the particular behavioral changes of domestication, assuming humans underwent these to reach their present state?

A scene from one of the best NOVA episodes:

Humans are more trusting of one another. Humans also have greater empathy and more sophisticated theories of mind than apes. There is also less aggression, at least towards the in-group if not conspecifics generally. I don’t think I will be accused of gender bias if I suggest that females are less aggressive than males. There is enough data to support this, and it is well associated with measurable hormone differences.

I remember once hearing of a study, which I cannot find right now, that reported upwards of 60% of the words spoken by people are not for communicating useful information at all, but are mostly gossip. If you believe that women talk more than men do (3) and that 60% should apply to them as well, this suggests that gossip and other kinds of social communication may actually be the primary purpose of language. Taken together with the ape study I have this hypothesis:

Nature has selected for less aggressiveness, and greater levels of sociality within the in-group. Especially for children, it became important to learn from mothers and other members of the tribe or community. This required that children be receptive and trusting, and that receptiveness came along with a certain gullibility. I am suggesting this is the origin of the “disposition A” I discussed in a prior post. Also, to the extent that these evolutionary changes are more pronounced in women it also suggests that they have been subject to a greater selective pressure in this direction. Humans had to evolve a system-wide substrate for the preservation of cultural mimetic information, and a perhaps unavoidable consequence of that was also a propensity for superstition and ritual.

There is unfortunately the sexist implication that women are better at learning from others at the expense of a capacity to explore new knowledge on their own, which I think legitimates the kind of sentiments expressed by Larry Summers(4). I won’t try to defend this – I don’t think there exists and there may never exist experimental data to back up an assertion that goes that far. This returns us to where the post started: without women participating equitably in the scientific process, their stories and their perspectives will go largely unexplored, or explored by men who would rather proliferate theories of females laying on their backs, waiting for males to come home with food (4).

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1. http://www.sciencemag.org/content/346/6208/405.full
2. http://humanorigins.si.edu/evidence/human-fossils/species/ardipithecus-ramidus
3. This is by no means a settled question in the literature despite my personal experience http://www.hsph.harvard.edu/news/features/do-women-talk-more-than-men/ .
4. http://bulletin.swarthmore.edu/bulletin-issue-archive/index.html%3Fp=145.html. The suggestion that males have a greater variance in scientific ability than females is one my hypothesis would be sympathetic too. Autism is more common among males, and this helps push them towards the far upper and lower ends of the bell curve. These are impossible things to quantify, though.
5. Owen Lovejoy: http://www.discovery.com/tv-shows/other-shows/videos/i-ardipithecus-i-males-become-providers/, Rebecca Solnit: http://harpers.org/archive/2015/06/shooting-down-man-the-hunter/1/