Proof from Morality (4)

The Golden Rule

Maat, the system of justice and morality used by the ancient Egyptians, was centred around this now-famous rule:

Do undo others as you would have them do unto you.

The Golden Rule is present in a wide variety of religions, like Daoism, Christianity, Buddhism, Islam, and Jainism, and was declared a common principal by 143 spiritual leaders in the “Parliament of the World’s Religions.” And yet Game Theory suggests it’s a bad way to live. On first blush it translates to “Always Silent”, which is easily suckered by an “Always Rat.” Indeed, “Always Silent” is usually the first strategy to die off in Axelrod’s competitions. So why does it keep popping up?

I think the likeliest reason is a hidden meaning. Consider this koan:

If you meet the Buddha on the road, kill him.

(Linji, the founder of the Rinzaisect)

Linji isn’t really asking you to commit murder, he’s saying that you are likely starting out on your spiritual journey with a biased view of enlightenment. In order to move further down this spiritual “road,” you must “kill” this false “Buddha” or vision before you can reach true knowledge.

I might be missing some hidden content within the Golden Rule. Perhaps it would be better translated as:

Do undo others as they do unto you.

Which turns it into “Tit-For-Tat.” I think this is not so much a re-interpretation as a full-on re-write, but many philosophers agree to this change. To quote M.G. Singer (who himself is quoting Hans Reiner):

The Golden Rule implies that ‘I should order my conduct consistently with my judgements of the conducts of others.’ In doing so it ‘presupposes a moral standard’ and also ‘gives us a standard to judge our own conduct by in referring us to our judgements of similar conduct on the parts of others.’ It thus refers us ‘to a norm that it does not… explicitly contain, but that each of us takes for granted.’ […] ‘we must have long ago acknowledged some norms to be valid… What we have in consequence is a moral a priori to order our conduct by; an a priori that is admittedly neither formulated or proven in the abstract, but that we still previously acknowledged to be valid in certain applications. Our acknowledging this,’ Reiner adds, ‘is of greater importance than any philosophic proof’.

(“The ideal of a rational morality,” pages 18-19)

Ah, so the Golden Rule itself is not a moral, but a reminder to treat everyone the same according to different morals that are already agreed upon by everyone. This last bit is a big flaw; once we stop agreeing on a common set of morals, his interpretation of the Golden Rule collapses. This can be fixed by creating a deity which in turn creates universal morals. Alternatively, we can use the combination of Game Theory and evolution that I outlined above, in which case this interpretation morphs into “Tit-For-Tat” without needing a deity.

Jeffery Wattles takes another approach:

  1. Treat others as you want others to treat you.
  2. You want others to treat you with appropriate sympathy, respect, and so on.
  3. Therefore, treat others with appropriate sympathy, respect, and so on.

Notice that our sense of what is appropriate  represents an estimate of value, an estimate that is adjusted in the process of thinking over the parity of self and other that is the primal assumption of the of the rule. The golden rule cannot be the supreme principle of morality in the sense of functioning as the sole normative axiom in a deductive system of ethics, because it cannot operate in a value vacuum.
(“The Golden Rule”, page 166)

Oh boy. Now the Golden Rule depends on the definitions of “appropriate” and “value,” as well as an underlying shared moral framework. Simply by shuffling around definitions and assumptions, Wattles could easily turn it into “Tit-For-Tat,” and indeed proceeds to do so.

Personally, I think this interpretation of the Golden Rule is most accurate, even though it’s rejected by many:

Do unto your neighbour as you would have them do unto you.

Here, “neighbour” does not have its modern meaning of “the person in the house next to you” or “everyone within a certain area.” Instead I’m using its original meaning, “the people you grew up with.” We’ve been spoiled in recent centuries by cheap mass transit and ample leisure time. Hunter-gatherers could move impressive distances, but they always travelled together as a tribe. Farmers and serfs were rooted to one spot, either due to the endless toil needed to grow crops, or the need to watch over food stores, so your children were usually nearby. The merchant class and nobility were the only exceptions, but they were a small minority and never referred to each other as “neighbour.”

In short, your “neighbour” was likely related to you, and definitely shared your religion and tribe. This situation led to the Jewish Ten Commandments, as an example, which only told you how to treat your fellow Jew.[120]

This interpretation creates a hole in the Golden Rule. How should we treat non-neighbours? We’ve only got two choices: fall back on other morals, or use our instincts. As I’ve shown, the latter is probably one of the “Simple Three.”

Hmm, so we have “Always Silent” to one group, and “Generous” or “Pavlov” to everyone else. Could the Golden Rule really be one of the “Secret Handshake”s from Southampton? It’s plausible; those algorithms were the only complex ones to beat the Simple Three, so they would offer an advantage if they every spontaneously popped up.

They might use a different “everyone else” rule, though. The SU group knew their strategies would be facing a diverse ecosystem, so they chose an “everyone else” that could cope with anything. In real life, interactions with an “everyone else” would be rare, maybe even one-time events, so it makes more sense to go with “Greedy Tit-For-Tat”[121] or even the best strategy for one-time play: “Always Rat.”[122]

If the Golden Rule really is a “Secret Handshake,” then any one or thing that implements it must have a way to identify itself. On the human scale, this could mean clothing, jewellery, body modifications like tattoos or piercings, or even behaviour. To cut down on the number of wolves in sheep’s clothing, it would help to make these displays outrageous, maybe even painful, so that only a true believer would have the stomach to perform or show them.

“Secret Handshake” assumed everyone was honest about their ID. That won’t fly in real life, so we should also expect some sort of enforcement system to ensure everyone acts like they promised they would. A group judicial process or a way to anonymously report cheats could be present, with the harshest punishment in either case being exile. People can be corrupted, though; it would be great if there was a way to observe everyone 24/7, or better yet look into their thoughts, that was paired with an incorruptible system of punishment.

Are there examples of “Secret Handshake” in human society? I’ll leave that for my chapter on the Popularity proof.

Clockwork

Back to the last objection: isn’t this duo of Game Theory and evolution somewhat cold and indifferent? Perhaps, but I don’t consider that a bad thing. I rely on instinct to keep me breathing and help me walk. In fact, most of my behaviour is mere instinct; is it so bad that some of my morality is also on autopilot too?

“Aha!,” you say, “he just admitted that some of his morality is not instinctual!”

It’s true, some moral decisions haven’t been “solved” via evolution. Should I buy a record from my favourite band, or copy it off a friend? Should the equality of women be actively encouraged by government programs, or passively encouraged via laws? Should state-run hospitals provide care to people who haven’t paid taxes or live in this country illegally? Should I drive to work and contribute to global climate change, or bicycle to work and put myself at greater risk of injury? We’ve never had to deal with those problems before, so the evolutionary process hasn’t “considered” the options and bred a solution into us. Perhaps a god is helping us with these trickier moral questions?

[120]  Need proof? Consider Exodus 32:15-28 in the Old Testament. Moses comes down from Mount Sinai with the newly-minted Commandments, only to find most of his family and tribe worshipping a golden calf. He proceeds to slaughter all 3,000 turncoats, despite just being given the commandment “Thou shalt not kill.” Under the modern definition of “neighbour,” that was madness. Those rogues had broken with tribal beliefs, however, so they were no longer neighbours in the traditional sense. The “no murder” commandment didn’t apply and thus Moses still had squeaky-clean morals when he was covered in his family’s blood.

[121]  I’m defining that as an initial Rat, followed by stock “Tit-For-Tat” with a random Rat tossed in occasionally.

[122]  With dense populations and cheap travel, these interactions become more common and so the rule for “everyone else” would be more like the Simple Three. Ever wonder why we push “tolerance for others” so much in modern times? I used to, until I wrote this chapter.

Proof from Morality (3)

Social Animals

One clue is that we see morality in other animals too.

Wild coyotes have play rules that ensure every pup is on equal footing. If one coyote can bite harder than another, it’ll hold back. If one is more dominant, it’ll send signals of submission to level or even reverse the social hierarchy. Pups that refuse to play by the rules are ostracised, to the point that they’re four times more likely to die.[115] The literature on elephants is full of heart-melting anecdotes, like the pack that deliberately slowed down to accommodate a disabled member, or the female elephant that swooped in to save another injured female from a male’s attack. Even rats can be remarkably chivalrous. A pair of them got stuck in a laboratory drain overnight. When they were found in the morning, only one was strong enough to drink or eat. This rat took a piece of food and placed it in front of the weaker one; as it nibbled on the gift, the strong one would tug it a short distance away, encouraging the weak one to crawl forward a little to resume its meal.

Can you guess where the stronger rat was tugging the food?

This does not rule out divine intervention, of course, it merely points out that any human-centred explanation of morality won’t do. Christianity, for instance, has traditionally claimed that only creatures of species Homo Sapiens Sapiens have a soul, and are thus blessed with intelligence, morality, or whatever noble trait the speaker wished. This black-and-white view fails in a world full of shades of gray.

While I can’t completely rule out the divine, I can provide a simpler explanation. In the introduction, I introduced Ockham’s Razor when deciding if oranges were gods. If I want to apply it here, I have to present a way for morality to develop that doesn’t need the help of a god. This gives us two theories for moral development and no evidence to prove either, the perfect situation to invoke Ockham and again make the god hypothesis useless.

The First Game

Let’s start with something abstract. Have you heard of the Prisoner’s Dilemma?[116]

Imagine you and a partner you’ve never worked with before team up to rob a bank. The police catch both of you, but not before you’ve stashed the loot in a safe place. They don’t have enough evidence for a conviction, so instead they split you up and press you to rat out your partner.

This puts you in a bind. Keeping quiet seems to be the smart move; so long as your partner stays quiet, both of you will be taking baths in your share of the money. But what if your partner rats you out as the ringleader? You’ll be making license plates while your partner can swim in both shares of the loot. It’d be better to rat them out instead and get your swimming trunks ready… unless they too rat you out. In that case, both of your swimming goggles will be sold at a police auction. You know your partner must be facing the same decision. What to do, what to do?

If you’re a logician, you always Rat out the other person. To understand why, I’ll summarize this game in a payoff table, with “points” instead of dollars:[117]

Your Partner’s Decision:

Stay Quiet

Rat You Out

You Earn:

They Earn:

You Earn:

They Earn:

Your Decision:

Stay Quiet

Victory Dances for All!

You’re screwed, big-time.

3

3

0

5

Rat Them Out

TOTAL VICTORY!!

everybody loses

5

0

1

1

Tally up the “You Earn” portion of each column. Since the total value for “Rat Them Out” row is greater than the “Stay Quiet” row, you stand to gain the most points by Ratting. This will also protect you from the worst-case of zero points, while opening up the best-case of five. Your partner knows all this, too, and thus is likely going to Rat on you anyway. It makes perfect logical sense.

And yet when you present this scenario to non-logicians, they usually Stay Quiet. For some reason, they trusted their partner to go for the best-case scenario, even though there was no logical reason for it. Logicians were perplexed, and launched several studies trying to figure out why humans were so willing to be so forgiving.

The most infamous was started by Robert Axelrod. Instead of asking people to play this game, he created several computer program “players” and gave each a different strategy. These were treated like bacteria floating aimlessly in a dish; two programs were picked at random to compete, and the awarded points went to their type of strategy. As each strategy earned or lost points, individuals of that type were added or removed from the “dish”. This is an important change; in the scenario above, the Prisoner’s Dilemma was played for a single round, not several. In addition, individual players were also granted the ability to remember programs they interacted with before and every choice that individual picked before, but weren’t allowed to know what strategy they were interacting with.

Axelrod then did something interesting: he turned his study into a competition by asking his peers to create strategies for the digital players. There were no restrictions on program length, so long as the submissions followed the above rules. He received fourteen strategies in total, ranging from the self-explanatory “Always Rat” and “Always Stay Quiet,” to complicated versions that used advanced statistical techniques to predict the likelihood of the next outcome and act accordingly. He added a fifteenth strategy to the mix, “Pick Randomly,” and let the simulation run.

The results were a shock. The most successful strategy was the simplest non-trivial one! “Tit-For-Tat,” submitted by Anatol Rapoport, just repeated what its challenger did last round. If there was no last round, it chose to stay quiet. No other strategy, no matter how complex, could beat it.

Somewhat taken aback, Axelrod shared the results publicly and asked for more challengers. This time, he received 62 submissions. Rapoport re-submitted “Tit-For-Tat,” with no changes.

After 3 million rounds, “Tit-For-Tat” still beat all comers!

Axelrod and other researchers have re-run this simulation, with various tweaks. If a player’s choices are occasionally flipped from “Quiet” to “Rat,” or vice versa, “Tit-For-Tat” is beaten by “Generous Tit-For-Tat.” The only difference between the two is that “Generous” occasionally ignores history and plays a “Silent;” this prevents it from falling into a cycle of retribution over a flipped choice. If digital players can remember their own past choices too, an even simpler strategy called “Pavlov” can rule the roost. If the two players didn’t play the same strategy last time (say one picked “Quiet” while the other chose “Rat”), “Pavlov” plays “Rat,” and in all other cases goes with “Quiet.” The reasons why it beats “Tit-for-Tat” are complicated, but “Pavlov” seems to encourage an “ecology” of strategies that allow it to rise to the top.

It’s important to note that while these three simple strategies dominate, they rarely stand alone. The usual result of these contests is a balanced ecology, with one or two big players and a number of smaller ones surviving on the edges.

The “Tit-For-Tat” duo and “Pavlov” have only been bested once. On the 20th anniversary of his first contest, Axelrod staged another. This time the winners we some clever entries from Professor Nicholas Jennings and others at Southampton University. When these programs encountered a new opponent, they played back a pre-set series of moves. If their opponent responded with a certain pattern of choices, they began acting like “Always Rat” or “Always Silent” to them. If not, they gave that player the “Generous” or “Pavlov” treatment.

If you know what strategy your opponent will take, any game becomes trivial. If your opponent will always stay “Quiet,” the best strategy is “Always Rat,” which earns you the most points per round. If you know you’re playing against your own strategy, “Always Stay Quiet” is better since it has the highest point earnings collectively. If up against “Always Rat,” “Always Rat” will minimize the damage.

While the procedure hid the strategy of each program from all others, SU’s entries exploited a loophole. By watching the first sequence of moves, they could spot what program they were up against, as well as broadcast what strategy they were using. SU’s entries traded short-term failures for long-term gain, and this edge was enough to catapult the “Secret Handshake” strategies to the top.[118] In contrast, the “Simple Three” treat everyone equally. This is one key to their success: they make no assumptions about their opponent, and thus can’t have those assumptions turned against them. There’s a cost to be paid, however. By treating everyone equally, they cannot exploit any differences between strategies.

Had Axelrod done another round of competition, none of the “Secret Handshake”s would have cracked the top 10. Why? Their advantage was based on an assumption: every program with a fixed opening sequence is honest. Now that their initial sequence of moves is public, another competitor could write a program that impersonates these winners, only to change its behaviour after it detects one of them has taken the bait. To combat this the Handshakes would have to change between rounds, and the only legal way to pull that off in Axelrod’s contest is to resubmit new programs each time.

We’re ready to move back to the real world.

The Prisoner’s Dilemma originally featured real people. It makes a lot of sense to bring them back in and watch the results. Under the same rules and restrictions, it turns out, we imitate “Generous” and “Pavlov.” And yet few of us have heard of the Prisoner’s Dilemma, let alone studied it. This also explains why we tend to Stay Quiet during the one-round version; all three simple strategies play that on the first round.

Remember the infant experiment? The puppets were engaged in a game very similar to the Dilemma, except it was impossible for both to lose. The baby didn’t participate that time, but instead had a preview of how each player would behave. When it was entered into the game via the food bowls, it took advantage and behaved like “Tit-For-Tat” on the second round; Rat on the puppet that had Rat-ted last time, and Stay Quiet to the one that had Stayed Quiet.

Variations on the Prisoner’s Dilemma are extremely common in the real world. Should I ignore that bacterium floating towards me, and risk being attacked, or should I pre-emptively start a battle? Will I hunt in a group and share my food, or hunt alone and hoard it? I’ve spotted a distant predator; should I put myself at risk by chirping in alarm, or stay quiet and hide? To play or snub? Attack or flee? Submit or defy? Our choice in each case effects our very survival.

This is evolution’s turf. Since behaviour can be partially controlled by our genes, we have been evolving solutions to these dilemmas for billions of years. It’s remarkable how closely the artificial and natural versions match; both result in populations where the majority use “Generous” or “Pavlov,” but a minority get away with “Always Rat” and a host of other less-than-optimal strategies.

Hopefully this also sheds light on an oddity I glossed over earlier. The total points awarded for mutual Quiet are greater than Rat/Quiet because that’s a closer match to reality. I share half my genes with my parents, siblings, and children, so helping them indirectly helps my genes spread as well. I get less benefit by helping others in my species, but keeping the gene pool diverse is still a net plus.[119] Therefore, both players get a minor bonus when they co-operate. There can even be some cross-species benefit; dogs provide us companionship, hunting skills, and early warning to a mutual predator, and we’re happy to return the favour.

Both players also get a minor bonus when they harm one another. While I’m worse for the encounter, at least the other player isn’t any better off and is less likely to threaten me in future.

Game Theory and evolution can explain a lot of moral behaviour. Why are we kind to strangers? Because altruism can pay off later. Why do we rarely lie and steal? Because we may get punished for it, by the victim or a third party, and if too many people do it everyone suffers. Why do people do it anyway? Because we can get away with it in small doses. Why are we fairly consistent in our moral choices? Because the best strategies are simple enough to be bred into our very bones. No higher power is needed for this, so no higher power should be assumed.

A common critique against this approach is that it fails to provide an absolute morality. It’s true, this morality only applies to anything that evolves. But do we need a moral system which accommodates for the experiences of rocks or solar systems?

If this approach seems greedy or short-sighted, sit tight. I need to cover a gaping hole before I move on.

[115]  “The Ethical Dog,” Scientific American Mind, March 2010

[116] This is a classic problem in Game Theory, developed by Merrill Flood and Melvin Dresher back in the 1950’s.

[117]  Note that if both of you co-operate, the total reward is greater than the total reward when there’s one winner and one loser, and if both of you Rat you yourself do better than if you alone lost. As you’ll see later, this tends to be the most interesting award system, and thus most studied.

[118]  Can you guess where the worst performers of that round came from?

[119]  This is why homosexual behaviour has been found in every species we’ve studied. Why they are very unlikely to have children, non-breeders make excellent uncles and aunts and thus benefit even the greediest gene. [Future HJH: It’s ONE reason, not THE reason. Biology is complex, so it should be no surprise if multiple reasons exist, some of which are not due to adaptation.]

Proof from Morality (2)

Two Big Objections

That brings up a good point. The Morality proof states quite clearly that morality can only come from a god. Is that really the case, however?

It cannot be, if the god in question is omnipotent:

  1. God X’s actions define a moral code.
  2. God X is omnipotent.
  3. God X can therefore do any action.
  4. God X is therefore capable of an immoral act.
  5. 4. contradicts 1.

There are only two ways to solve this dilemma: give up on god X providing our moral basis, or give up on that god being omnipotent. The last way certainly seems the most sensible, even if it opens us up to questions of what that god can and cannot do.

A similar argument was made by Plato 2,400 years ago. Rather than invoke omnipotence, in the Euthyphro dialogue he had Socrates invoke causality: either the gods are good because they act according to a moral code, or they are good by definition and thus form a moral code.

Here’s the problem: only one of those possibilities can be true, yet they have radically different outcomes. If a god is only following a pre-existing moral code, then it must be constrained by that code as much as we are. We’d be better off ignoring or disputing the moral pronouncements of this god, and examining the moral code directly. Most theists reject this possibility out-of-hand.

Instead, let’s go along with the idea that a god’s actions provide our moral grounding. Where does that get us?

To a very scary place, I’m afraid. That means that every action a god does is moral. Period. So when your god slaughters thousands of people, condones slavery, and pushes actions based on faulty reasoning, you have no choice but to call it moral, even as you condemn other human beings for doing the same actions. A prime example of this comes courtesy of William Lane Craig, who was asked about an instance of genocide in the Old Testament, specifically Deuteronomy 20:10-18:

God has the right to take the lives of the Canaanites when He sees fit. How long they live and when they die is up to Him.

So the problem isn’t that God ended the Canaanites’ lives. The problem is that He commanded the Israeli soldiers to end them. Isn’t that like commanding someone to commit murder? No, it’s not. Rather, since our moral duties are determined by God’s commands, it is commanding someone to do something which, in the absence of a divine command, would have been murder. The act was morally obligatory for the Israeli soldiers in virtue of God’s command, even though, had they undertaken it on their on initiative, it would have been wrong.

On divine command theory, then, God has the right to command an act, which, in the absence of a divine command, would have been sin, but which is now morally obligatory in virtue of that command.

(“Slaughter of the Canaanites.” )

There are a number of rebuttals to the Euthyphro dilemma. This is a typical example:

The Christian rejects the first option, that morality is an arbitrary function of God’s power. And he rejects the second option, that God is responsible to a higher law. There is no Law over God.

The third option is that an objective standard exists (this avoids the first horn of the dilemma). However, the standard is not external to God, but internal (avoiding the second horn). Morality is grounded in the immutable character of God, who is perfectly good. His commands are not whims, but rooted in His holiness.

Could God simply decree that torturing babies was moral? “No,” the Christian answers, “God would never do that.” It’s not a matter of command. It’s a matter of character.

(“Euthyphro’s Dilemma,” Gregory Koukl. )

So absolute morality isn’t external to God, nor determined by God’s actions, but instead equal to God. Which means it must be determined by God’s actions, but that’s OK, because God would never order us to do anything immoral.

No really, this is not only a popular counter-argument, but the most popular one by my reckoning.

The Euthyphro dilemma is actually a false dichotomy. That is, it proposes only two options when another is possible. The third option is that good is based on God’s nature. God appeals to nothing other than his own character for the standard of what is good, and then reveals what is good to us. It is wrong to lie because God cannot lie (Titus 1:2),[108] not because God had to discover lying was wrong or that he arbitrarily declared it to be wrong.

(“What is the Euthyphro dilemma?,” Matt Slick.)

There is, however, a third option. As Christians we should affirm both God’s sovereignty and His non-derived goodness. Thus, we don’t want a standard that is arbitrary nor one that exists outside or above God. Fortunately, God is both supremely sovereign and good. Therefore, God’s nature itself can serve as the standard of goodness, and God can base His declarations of goodness on Himself. God’s nature is unchangeable and wholly good; thus, His will is not arbitrary, and His declarations are always true. This solves both issues.

(“What is Euthyphro’s Dilemma?,” http://www.gotquestions.org/Euthyphro-Dilemma.html )

But it might be permissible to lay down two negations: that God neither obeys nor creates the moral law. The good is uncreated; it could never have been otherwise; it has in it no shadow of contingency; it lies, as Plato said, on the other side of existence. […] But we, favored beyond the wisest pagans, knows what lies beyond existence, what admits no contingency, what lends divinity to all else, what is the ground of all existence, in not simply a law but also a begetting love, a love begotten, and the love which, being between these two, is also immanent in all those who are caught up to share the unity of their self-caused life. God is not merely good, but goodness; goodness is not merely divine, but God.

(“Christian Reflections,” C.S. Lewis. pg. 80)

There are other approaches, most notably this:

But the view which I am putting forward takes the first horn form for some obligations and the second for others. I suggest that we ought not to rape, or break a just promise (that is one which we had the right to make), whether or not there is a God; here God can only command us to do what is our duty anyway. By contrast only a divine command would make it obligatory to join in communal worship on Sundays rather than Tuesdays.

(“God and Morality,”  Richard Swinburne . Think 20, Vol. 7, Winter 2008)

Unfortunately, while dividing up morality into “necessary” and “contingent” sections seems like a good dodge, some thought reveals that it introduces more problems than it solves. You can’t rape if there’s no such thing as a universe, and most theists argue their god is responsible for the creation of universes; hence, a “necessary” moral truth is actually contingent on the existence of a god! Swinburne also tries to answer the obvious question, namely why we have to bother with the “contingent” moral codes at all, and offers up three reasons: they make good reminders of “necessary” morals, they help us work together, and they get us in the habit of doing good. All three can be done in a purely secular fashion, without the need for a god, which makes us justified in ignoring the divine portion.

Worst of all, the reliance on holy texts means this moral code is up for interpretation. Let’s return to the 613 Jewish mitzvot, specifically numbers thirty-three and thirty-four,[109] which are in this passage.

 If thou shalt hear tell concerning one of thy cities, which the LORD thy God giveth thee to dwell there, saying:
‘Certain base fellows are gone out from the midst of thee, and have drawn away the inhabitants of their city, saying: Let us go and serve other gods, which ye have not known’;
then shalt thou inquire, and make search, and ask diligently; and, behold, if it be truth, and the thing certain, that such abomination is wrought in the midst of thee;
thou shalt surely smite the inhabitants of that city with the edge of the sword, destroying it utterly, and all that is therein and the cattle thereof, with the edge of the sword.
And thou shalt gather all the spoil of it into the midst of the broad place thereof, and shall burn with fire the city, and all the spoil thereof every whit, unto the LORD thy God; and it shall be a heap for ever; it shall not be built again.

(Deuteronomy 13:13-17, Pentateuch. JPS 1917 translation)

The thirty-third mitzvot, specifically, calls for the burning of all cities that don’t worship YHWH. On the surface, this seems like a pretty clear-cut order to commit genocide. But what does it mean for YHWH to “give” you a city? Do you need the official stamp of a council of rabbis, or can it be revealed to you in a vision? Since YHWH can secretly alter the behaviour of people,[110] it’s also possible he could have steered you towards wherever you’re living right now, and this implicitly “give” you whatever patch of land you happen to be sitting on.

And how many believers in a false religion[111] do you need in a city before you burn it down? This passage talks about converting “the” inhabitants, which usually implies all of them, but it seems odd to wait until every last person worships another god before bringing on genocide, when later mitzvot make it clear that the same crime committed by a single person is worthy of death.

 If there arise in the midst of thee a prophet, or a dreamer of dreams–and he give thee a sign or a wonder,
and the sign or the wonder come to pass, whereof he spoke unto thee–saying: ‘Let us go after other gods, which thou hast not known, and let us serve them’;
thou shalt not hearken unto the words of that prophet, or unto that dreamer of dreams; for the LORD your God putteth you to proof, to know whether ye do love the LORD your God with all your heart and with all your soul.
After the LORD your God shall ye walk, and Him shall ye fear, and His commandments shall ye keep, and unto His voice shall ye hearken, and Him shall ye serve, and unto Him shall ye cleave.
And that prophet, or that dreamer of dreams, shall be put to death; because he hath spoken perversion against the LORD your God, who brought you out of the land of Egypt, and redeemed thee out of the house of bondage, to draw thee aside out of the way which the LORD thy God commanded thee to walk in. So shalt thou put away the evil from the midst of thee.

(Deuteronomy 13:2-6,[112] Pentateuch. JPS 1917 translation)

With so many billions on the street it would be tricky to enforce the prohibition against resettlement, or the thirty-fourth mitzvot. Most cities began where they were for a reason, such as a close proximity to water or excellent soil. By forcing everyone to settle elsewhere, you’re not only giving up prime real-estate, this exodus would require destroying precious farmland to house the refugees. Note as well that YHWH explicitly bars resettlement of any ravaged city at any future time, thus devout Jews would have to guard all this rubble for an incredible length of time.[113]

Oddly enough, I don’t know of a single devout Jew who actually follows these two mitzvot. I’m quite thankful for that, but I do find it peculiar that so many Jews would interpret that passage to mean anything other than genocide.

We can generalize this problem to all religions. Even if your god possesses an absolute moral code, and even if it has communicated that code to us in some way, the interpretation of that code is the responsibility of human beings, who cannot possess an absolute moral code (because otherwise they’d have no need for this god’s moral code and the proof from morality falls apart). If it is possible for human beings to interpret, however, then it must be possible to misinterpret, and thus we cannot be sure we’re following this absolute moral code in totality; there will always be a small chance that we’re getting some part wrong. This is a huge problem, because every method of divine enlightenment involves a human middleman.

It’s as if someone crafted a perfect technique for making pottery, but only told people who were bad at the task. The results are guaranteed to be less than perfect.[114] So even if an absolute moral code existed, we could never follow it.

Or prove it, for that matter. “Absolute” implies that all possible observers would agree, given sufficient information. So let’s say we ask one hundred people if murder is bad, and all of them agree. Have we proven all observers agree? Nope. So let’s ask one billion people, and let’s say all of them agree. We still haven’t demonstrated everyone agrees. So let’s ask every single human being that has existed or will exist on this planet. Is that everyone? Nope, we still haven’t asked people who could have existed, but didn’t. Maybe one of them disagrees? It would destroy our assertion of having an absolute consensus on murder.

To many, this is a paradox. If there is no absolute moral code, why do we agree to such a large degree? Why do we consistently agree that murder is a bad idea, or that cheating is wrong?

[108] Actually, He can. See Jeremiah 20:7 and 2 Thessalonians 2:11.

[109] I’m using Maimonides’ list and ordering. A number of rabbis have developed their own mitzvot lists, some of which disagree, but Maimonides’ is the most accepted within the Jewish community.

[110] In Exodus 4:21, 9:12, and 10:20 (amongst others) YHWH hardens Pharaoh’s heart. Of course, according to Exodus 8:32 and 9:34 (amongst a few more) Pharaoh hardens his own heart. I’ve already mentioned 2 Thessalonians 2:11-13, too, where God deludes people into believing lies.

[111] Religion may not be necessary, either; while this passage explicitly mentions worshipping the wrong gods, that could be considered a metaphor for idolatry in general. And some rabbis [INSERT CITATION HERE] hold that any reproduction of the human form is a type of idolatry.[FUTURE HJH: Almost!] So in the most extreme interpretation, any city, town or village where someone has a photo or drawing of a human on their wall must be burnt to the ground.

[112] That’s not a typo, mitzvot fourty-three does refer to a passage which proceeds thirty-three and thirty-four. Maimonides arranged his list by category, not order.

[113]  Current estimates suggest the oceans will boil away in 500 million to one billion years, and that in four billion or so our Sun might expand out and swallow our planet. The former might not kill off all life on this planet, depending on how sophisticated the technology of the day is, and the second isn’t guaranteed to happen. Those Jewish guards may want to pack a lunch…

[114]  I’ll reuse this argument in the proof from holy texts, by the way. Adjust your reading plans appropriately.

Proof from Morality (1)

A hot topic in psychology is the study of infants.

We had great difficulty finding a way to probe their minds. How do you communicate with something that cannot talk, after all? In the 1980’s, scientists found a simple solution: if an infant is puzzled, they’ll stare at something longer than if they understood it.

For instance, put two dolls behind a curtain, then pull away the curtain. Five-month-old infants will pay little attention if there are two dolls behind the drapes, but will take notice if one or three dolls are sitting there. This behaviour only makes sense if they have some basic counting skills built-in at birth.

Or, stage a puppet show instead. Have the puppets nicely pass a ball to each other for a while, only to have one steal the ball and run off-stage. Now set both puppets in front of the infant, each with a bowl of food placed in front, and encourage the child to take a treat. The vast majority of the time, infants will take from the bowl in front of the greedy puppet. Clearly, they wanted to punish this amoral muppet.[104]

But how can this be? Children that young don’t understand language, so they can’t have learned this from an adult. This sense of morality must be built-in. And who better to do the building-in than a god?

The earliest religions we know of seem to agree. Ma’at, the ancient Egyptian code of ethics, is a prime example.

Maat is right order in nature and society, as established by the act of creation, and hence means, according to the context, what is right, what is correct, law, order, justice and truth. This state of righteousness needs to be preserved or established, in great matters as in small. Maat is therefore not only right order but also the object of human activity. Maat is both the task which man sets himself and also, as righteousness, the promise and reward which await him in fulfilling it.

(Siegfried Morenz, “Egyptian Religion.” Cornell University Press, 1973. pg. 113)

The earliest written records of Ma’at date back to 2600BCE. The Sumerians had a similar system involving “underworld judges” since at least 2900BCE. This is as far back as we can reliably look, as these two civilizations were kind enough to write down their morals for us.

Moral Quandaries

Wait wait wait, we’re missing something here. Before we can properly discuss morality, we need to nail down what a moral is.

That seems simple enough, as we’re handed morals all the time via stories. In Shakespeare’s play “Macbeth,” Lady Macbeth is so devoted to her husband that she practically murders the king for him, thinking that because it was prophecized to happen everything would turn out fine. It doesn’t; she kills herself out of guilt over the murder, and her husband’s head winds up on a pike. The moral of the story is: don’t kill people, even if it’ll get you a head.[105]

In part, then, a moral is a description for how to behave (or how not to behave) in a given situation. To be moral, or to be “good,” is to follow that description. But there’s another aspect to it as well; the night of the murder, Macbeth sees a ghostly dagger, and others note strange behaviour from the animals and weather. Back in the 1600’s, that could only mean one thing: something bad or immoral was going to happen to the king, and the gods didn’t approve of it. Compare this with Macduff’s beheading of Macbeth near the end of the play; another king is killed, and yet this time nature doesn’t kick up a fuss, indirectly hinting that it approves. So morals aren’t simply rules you follow, but rules you should follow.

Should? According to who or what?

And in that word, we see exactly why the religious love bringing up morality. A moral must have some justification for it, presumably from something or one greater than the entities that must live by that moral. I could declare that everyone should give me a portion of their earnings, because I’m just that awesome, but the justification for that moral dies along with me. There’s also a chance that I may be mistaken about my awesomeness, or inventing it in order to line my pockets. I could even change my mind! We need something more stable than an individual to anchor our morals to, and yet even human culture and society can change dramatically over time. An external, unchanging entity would be an ideal anchor, such as a god.

There’s still one more axis to consider, though. During a royal banquet, the newly-crowned Macbeth has his seat taken by the ghost of his former rival, Banquo. Nevermind the action on stage, take a step back and ask yourself a more basic question: is this banquet moral?

That question seems terribly strange. It’s expected of kings to hold banquets from time to time, and pretty much required of them to host one after their coronation. If someone has no choice in an action, how can morality enter into it?

Aha! We’ve finally clinched our definition: a moral is a description of how something should (or shouldn’t) behave in a certain situation, given multiple choices. Eating does not involve morality, since you have no choice on the matter.  Your choice of what to eat is quite different, provided you have more than one choice. Even then, if none of those choices have been approved or disapproved in some fashion, then we’re not making a choice based on morality after all.

This definition opens up new possibilities, too. Suppose we were to walk into a deserted village, poking our heads into the deserted doors. We’re surprised to find the interiors were kept remarkably clean when they were occupied, which is quite unlike all others we find from that time. We’ve got two-thirds of morality in place already: from how consistent this pattern is, we can be pretty confident there was a description of how to behave, and from this village’s neighbours we know they had multiple options. The only thing missing is a “should,” but again the consistency of this behaviour suggests the original occupiers of this village had one.

If you agree to this, we can push back the first evidence of morality to the Çatalhöyük settlement in Turkey, which was occupied between 7500 and 5700 BCE.[106]

Can we go farther? Many archaeologists, including Klaus Schmidt, claim that a site called Göbekli Tepe may actually be the first religious temple.

In the pits, standing stones, or pillars, are arranged in circles. Beyond, on the hillside, are four other rings of partially excavated pillars. Each ring has a roughly similar layout: in the center are two large stone T-shaped pillars encircled by slightly smaller stones facing inward. The tallest pillars tower 16 feet and, Schmidt says, weigh between seven and ten tons. As we walk among them, I see that some are blank, while others are elaborately carved: foxes, lions, scorpions and vultures abound, twisting and crawling on the pillars’ broad sides. […]
And partly because Schmidt has found no evidence that people permanently resided on the summit of Gobekli Tepe itself, he believes this was a place of worship on an unprecedented  scale—humanity’s first “cathedral on a hill.”

(Andrew Curry, “Gobekli Tepe: The World’s First Temple?“ Smithsonian magazine, November 2008.)

Again, we find hints of morality; almost all deities encourage their worship, implicitly approving of it, and yet we have the choice of not worshipping. If that place truly was a temple, then our evidence of morality begins at roughly 9500 BCE. To put that date in context, it’s only a thousand years after the last major ice age ended, right about when we learned how to farm, a thousand years before we invented numbers, six thousand before we discovered copper and writing, and eight thousand before Moses was given the 613 mitzvot[107] by YHWH, according to orthodox Judaism.

[104]  “The Moral Life of Babies,” the New York Times Magazine, May 5th,  2010.

[105] Sorry. Oh, and while I have your attention: I’m going to be discussing key plot points for the next few paragraphs. Spoiler alert!

[106]  http://www.catalhoyuk.com/library/goddess.html . Search for “clean.”

[107] Commandments of behaviour given to you by YHWH. Oddly enough, despite sharing the same holy text, despite Jesus claiming all old Jewish laws apply to Christians (Matthew 5:17-20), despite Jesus only naming six (Matthew 19:16-19) or two (Matthew 22:37-40) commandments explicitly, in violation of Jewish (Simon Glustrom, The Myth and Reality of Judaism, pp 113–114) and Christian (James 2:9-12) tradition that every commandment is important, Christians only recognize ten commandments as absolute divine law. And even then, they ignore the one about sacrificing your first-born (Exodus 34:19-20). Go figure.

76 days

I was wondering how long it would take for Trump to start a war to prop up his approval ratings, and I may have just gotten my answer.

The operation, which the Trump administration authorized in retaliation for a chemical attack killing scores of civilians this week, dramatically expands U.S. military involvement in Syria and exposes the United States to heightened risk of direct confrontation with Russia and Iran, both backing Assad in his attempt to crush his opposition.

President Trump said the strike was in the “vital national security interest” of the United States and called on “all civilized nations to join us in seeking to end the slaughter and bloodshed in Syria. And also to end terrorism of all kinds and all types.”

“We ask for God’s wisdom as we face the challenge of our very troubled world,” he continued. “We pray for the lives of the wounded and for the souls of those who have passed and we hope that as long as America stands for justice then peace and harmony will in the end prevail.”

On the surface, that looks like it could trigger a war with Russia. But:

The Pentagon has confirmed it used a hotline for minimising the risk of aerial combat between US and Russian jets in eastern Syria to alert Russia of the strike against its Syrian client. The Russians are sure to have routed that warning to Assad, raising immediate questions about what the strike will have accomplished, and also signalling that the US does not seek escalation.

The sun is coming up on Russia, so we’ll quickly learn how accurate that is. Still, there’s good reason to think this won’t snowball into war, as well as good reason to think this is Trump shouting “WOLF!!” and pointing in the other direction.

Initial reports from Russia aren’t looking good.

Russia is waking up to news of the strike – though we know military channels were used to alert Moscow before the missiles were launched – and reaction so far has been hostile.

State news agency RIA quoted Viktor Ozerov, head of the defence and security committee at the Russian upper house of parliament, saying the US strikes could undermine the fight against terrorism.

Ozerov said Russia would call for an urgent meeting of the UN security council:

This [the attack] could be viewed as an act of aggression of the US against a UN nation.

In its first public response to the airstrikes, the Kremlin has issued a strong statement condemning the US move as “aggression against a sovereign nation”.

Moscow said the strikes had been carried out on an “invented pretext” and claimed the Syrian army did not have chemical weapons.

The strikes, it said, would do “significant damage to US-Russia ties” and created a “serious obstacle” to creating an international coalition to defeat Isis.

Russian president Vladimir Putin, the Kremlin said, views the strikes as an attempt to deflect world attention from civilian deaths in Iraq – where at least 150 people died in a series of coalition airstrikes in Mosul last month.

This could get ugly, quick, and it’s all for nothing.

Proof from Logic and Dualism (4)

You’ve Got to Have Soul!

This dismissal of a bridged consciousness and dualism strike at the heart of another key part of religion.

I’d argue that souls, instead of god, are the common thread between religions. Every religion I’ve encountered has them, no matter how many gods they worship:

And Jehovah spake unto Moses, saying,

When thou takest the sum of the children of Israel, according to those that are numbered of them, then shall they give every man a ransom for his soul unto Jehovah, when thou numberest them; that there be no plague among them, when thou numberest them.

(Exodus 30:11-12, Old Testament, American Standard Translation)

I bow down to those who have reached omniscience in the flesh and teach the road to everlasting life in the liberated state.
I bow down to those who have attained perfect knowledge and liberated their souls of all karma.
I bow down to those who have experienced self-realization of their souls through self-control and self-sacrifice.
I bow down to those who understand the true nature of soul and teach the importance of the spiritual over the material.
I bow down to those who strictly follow the five great vows of conduct and inspire us to live a virtuous life.
To these five types of great souls I offer my praise.

(The first six lines of the Namokar Maha Mantra, the “universal” prayer of Jainism)Never is he (Soul) born, nor does he die at any time, he has never been brought into being, nor shall come hereafter; unborn, eternal, permanant and ancient (primeval). When the body is slain, he is not slain. \
O’ Arjunaa, know this soul to be eternal, undecaying, birthless and indestructible. A person who knows him to be so — whom can he slay or cause another to slay.
As a man casts off worn-out garments and puts on new ones, so the embodied soul casts off the worn-out body and enters other new ones.

(Chapter 2, verses 20-22, from Srimad Bhagavat Gita, a Hindu holy text)

The concept of the soul requires two things, that consciousness be detachable from the brain, and that this consciousness have some non-material place to inhabit. With both in place, death becomes an annoyance instead of a finality, thus evaporating the biggest fear of any conscious organism. As an added bonus we can bolt on a system of punishment, to take care of anyone who got away with murder while alive.[102]

In some religions this non-material realm sounds suspiciously like the material one:

Lo! those who kept their duty dwell in gardens and delight,
Happy because of what their Lord hath given them, and (because) their Lord hath warded off from them the torment of hell-fire.
(And it is said unto them): Eat and drink in health (as a reward) for what ye used to do,
Reclining on ranged couches. And we wed them unto fair ones with wide, lovely eyes.
And they who believe and whose seed follow them in faith, We cause their seed to join them (there), and We deprive them of nought of their (life’s) work. Every man is a pledge for that which he hath earned.
And We provide them with fruit and meat such as they desire.
There they pass from hand to hand a cup wherein is neither vanity nor cause of sin.
And there go round, waiting on them menservants of their own, as they were hidden pearls.

(Sura 52:17-24, The Qur’an, translated by M.M. Pickthall)

After these things I saw, and behold, a door opened in heaven, and the first voice that I heard, [a voice] as of a trumpet speaking with me, one saying, Come up hither, and I will show thee the things which must come to pass hereafter.
Straightway I was in the Spirit: and behold, there was a throne set in heaven, and one sitting upon the throne;
and he that sat [was] to look upon like a jasper stone and a sardius: and [there was] a rainbow round about the throne, like an emerald to look upon.
And round about the throne [were] four and twenty thrones: and upon the thrones [I saw] four and twenty elders sitting, arrayed in white garments; and on their heads crowns of gold.

(Revelations 4:1-4, New Testament, American Standard Translation) [103]

In others, this non-material realm is never described, or slightly inconsistent:

In coming and going, birth and death an apostate loses honour.
By serving the True Guru man attains to eternal peace and his light merges with the Supreme Light.
The service of the Sat [True] Guru is extremely ease-bestowing and by it one obtains the boon that he desire.
By placing Lord God in the mind continence, truthfulness and penance are obtained and the body becomes pure.
Such person ever remain happy day and night and procures peace by meeting the Beloved.
I am devoted unto those, who have sought the protection of the True Guru.
In the True Court they obtains true honour and are easily absorbed in the True Lord.
Nanak, through associating with the society of the Exalted Guru one meets the Lord by His grace.

(from pg. 31 of the Sri Guru Granth Sahib, primary holy text of the Sikh, as translated by Bhai Manmohan Singh)

The exceptions, most notably deism and to some degree pantheism, lean on dualism instead. They can’t rely on the supernatural, but still yearn for a connection to something greater than themselves. Invoking a world of ideas allows them that comfort, without having to return to the messy contradictions of a traditional faith.

If consciousness is anchored to the brain, and a perfect world of the intellect is impossible, then dualism is as likely as an afterlife with a couch.

[102] I’ll develop this more in the Popularity proof, when I propose an explanation for religion’s origins.

[103] To add to the confusion, both Islam and Christianity have an different version of “heaven” in some sects. Instead of an eternal paradise after death, you decompose and lose consciousness until the end times, at which point all the good little believers will be given new bodies and brought back to life. This version doesn’t require souls at all.

You!

Who would you like to signal boost?

Today is Trans* Day of Visibility, and I have a gaggle of people and resources to share. Two web comics I follow are Rooster Tales and Trans Girl Next Door, which provide a great mix of silly and serious. On the educational side, TransAdvocate has been an excellent read, a mix of rigorous scholarship and activism. Zinnia Jones is in the same vein, and the Gender Analysis series she helped start is a must-see. And of course, Shiv’s blogging is worth highlighting.

Proof from Logic and Dualism (3)

Dualism

These effects aren’t limited to brain damage. Just over four percent of all humans are synaesthetic, which means that two separate regions of their brain link up more strongly than usual. The combinations seem limitless: some will see shapes when they taste anything, or hear sounds when they see something move, or their numbers will appear coloured. We know they aren’t faking it, because we’ve handed them a test like this:

Can you spot all the twos mixed in with the fives?

Most people[B] take about ten seconds to find all the 2’s mixed in with the 5’s. Most grapheme-colour synesthetes will glance at it and say “the 2’s form a square.” These people experience the world quite differently,[96] which has been confirmed by many tests like the above. We’ve also used brain scanning techniques to peer inside the skulls of synesthetes, and we find they’re wired differently in exactly the way our maps predict.

Einstein was infamous for his thought experiments, and when they cracked open his skull they spotted an enlarged inferior parietal lobe,[97] which is linked to spatial reasoning and visualization. Christian Gaser and several other researchers have found that professional musicians have differently structured brains than the rest of us. The areas responsible for hearing, as well as motor and spatial control, are physically larger.

Admittedly, none of the above is a slam-dunk debunk of a bridged consciousness. Nothing ever could be, so long as we have no concise definition of “consciousness.”[98] This fuzziness is exploited by those who are unsettled by the strong links between consciousness and the brain. “All that may be true, but at what point do I ‘see’? At what point does the objective sensory input become a subjective colour?”

The first question’s answer is “wherever you want.” Tell me: when does bread stop being dough, and start being bread? Surely not when the ingredients are mixed together, nor when it’s placed in the oven. It can’t be when it’s removed from the oven, since there’s no difference between the instants before it was removed and the instant after, and besides the inside is still being baked by the warmer outside. It can’t be when it has cooled to room temperature, because it was edible before then. It can’t be when the lump was first edible, because that’s a subjective measure that varies by person.

Face it, bread is much too complex to be understood by science. It must be a divine product!

What’s really going on here is that “bread” and “dough” are only probabilistic definitions. They only work in certain situations, but those situations pop up often enough to justify the definitions. Push either too far, and they’re guaranteed to fail. “Sensory input” and “seeing” are no different.

The second question is a little harder to answer. Christof C. Koch at Caltech found a “Halle Berry” neuron in an epilepsy patient. This little thing got excited whenever its owner was presented with a photo of Halle Berry, or a drawing of her, or even just her name. This neuron isn’t in everyone, of course, and almost certainly isn’t in the same spot in another person who recognizes that actress. And don’t let my poor phrasing fool you, the only difference between it and the neuron two spots over is which connections it has. The neurons on the other ends of those links have already marked the input as “person,” “female,” “known entity,” and so on. The entire length of this patient’s nervous system, from the ganglion in the back of the eye all the way down to this little neuron, has been gradually abstracting that image/picture/name of Halle Berry.

The only question left is how abstract we have to get to satisfy your definition of “subjective.” Once that’s done, we can zero in on one or more brain structures.

The Limits of Logic

Even if our consciousness doesn’t come from this second world, we can at least take some comfort in knowing it exists as the source of perfection and order.

Or can we? This half of the argument suffered two major blows in the past century, thanks to Kurt Gödel and Alan Turing.

Before those two were born, logicians had unearthed a crisis. They were probing the foundations of mathematics, and found it wasn’t as solid as they wanted. How were numbers constructed? Why did the basic math operations work? Could more complex operations be counted on? These are not trivial questions, since science heavily depends on math to measure and predict the world. Any weakness in one could topple the other. That anxiety triggered a century of search for the absolute fundamentals of math, which reached its pinnacle when Bertrand Russell and Alfred Whitehead took 362 pages to prove

1 + 1 = 2

Not only did the uncertainty refuse to leave, but to their horror it crept into logic as well. Epimenides of Crete was one of the first to discover the basic problem, albeit inadvertently:[99]

They fashioned a tomb for thee, O holy and high one
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in thee we live and move and have our being.

(Epimenides, Cretica, circa 600BCE)

Or, without the poetry:

I, as a Cretan, know that all Cretans are liars!

If Epimenides is lying, then Cretans tell the truth. But this is impossible, since he is Cretan. He must be telling the truth, then… but that would mean Cretans are liars, including Epimenides! This paradox has an easy solution (Cretans could be a mix of liars and truth-tellers), but it doesn’t take much thought to come up with a stronger version:

This statement is false.

Variations of this paradox were found in the rules of logic, and every attempt to remove them just created more. It was quickly becoming an embarrassment. Many mathematicians and logicians were drawn to the problem, hoping for a solution that put math on solid ground.

Instead, Kurt Gödel proved the ground would always be unstable. In his two Incompleteness Theorems, he noted that you could translate any group or system of mathematical statements into numbers. Since the results had a finite digit count, you could create a method that would take in a number and tell you if the original math statements were true or false. Since this method itself was a mathematical statement, it too had a number. Feed the method’s translated number to itself, and BANG, a contradiction popped out: this method cannot determine its own truthfulness.

Worse, the details didn’t matter. No clever transform could save the day, and every mathematical statement can be transformed. There were only two choices: ensure that this truth-evaluating method was not within the mathematical system you’re using, making it impossible to ever prove that every statement is true or false, or accept that your math rules will have contractions. It was the logical equivalent of a rock and a hard place.[100]

As mathematicians were freaking out over this, Alan Turing made things worse. Gödel’s Theorem focused on proving things true or false; it said nothing about whether all statements could be proven, period.

To study this tougher problem, Turing invented a simple “machine” which would later be named in his honour. These “Turing Machines” were basically an ideal computer,[101] no more than an infinite storage space for symbols paired with a set of instructions for modifying those symbols. Once you set a machine in motion, there were two outcomes: it would eventually stop running, or it would carry on forever. Turing now pondered if there was a way to examine a machine’s instructions to determine which way it would go.

The answer, surprisingly, was no! By using a route similar to Gödel’s, he showed that no matter what sort of method you used, there were always some machines that stopped but couldn’t be proven to do so.

As if that wasn’t bad enough, he also reinforced Gödel’s findings. Let’s define two more conditions: if a Turing machine halts, and there are no symbols in storage, we say it “accepted” the input. If the machine halts with any other configuration, we say it “rejected” the input. Suppose you handed me a storage space and a set of instructions for a Turing machine; could I tell you if the machine would accept or reject the tape? This scenario is Gödel’s Theorem in another form, and unsurprisingly Turing came to the same conclusion as Gödel.

Gödel and Turing shattered the idea of mathematical and logical perfection. Dualism’s proposed universe of ideas is a self-contradicting mess, at best. If we instead view this “universe” as something that emerges out of the material world, those contradictions make more sense. The lumps of matter from before are only additive down to a certain level, at which point reality gets very ugly and our abstractions break down. We should have expected the ugliness others have found in logic, in fact, since our abstractions deliberately over-simplify real life and thus are not guaranteed to be as consistent!

[96]  Having said that, all humans are partial synesthetes. Present us with two squiggles in a “foreign language,” ask us to guess which is “titi” and which is “bouba,” and the vast majority will assign the pointy shape the harsh-sounding name “titi.” The big difference between the typical human and a synesthete is the latter has a stronger, conscious connection.

[97]  Move your hand up your head a hand width, so one edge of it runs along the very top. That’s the parietal lobe, and the lower half of your palm is covering the inferior parietal.

[98]  I encounter the same problem with the intelligence proof, so in the interest of not boring this book out of your hands, I won’t tear “consciousness” apart in the same way.

[99]  I don’t think he did it on purpose. He believed, contrary to most Cretans, that the god Zeus was immortal. His poem was likely a rant against the foolish beliefs of his countrymen. Yes, I’m snickering, why do you ask?

[100]  You might be tempted to claim this impossibility for god. Unfortunately, any god that could defeat Gödel must be partially irrational, yet the laws of nature seem to be consistent and rational. That’s tough to reconcile.

[101]  Actually, Turing outright invented the modern computer. Before him, the non-human computer was dedicated to a single task, like adding numbers or calculating bombshell trajectories. His work, along with Von Neumann’s, showed that you could make them capable of any math task, no matter how complex. This was so important, I think it overshadowed his other big accomplishment: winning World War 2 for the Allies!

[B] Past-me had written “ordinary people” here. Tsk, tsk.

Proof from Logic and Dualism (2)

Elegant, According to Whom?

I suppose you’re curious about what these mythical four equations look like. Fortunately, they’re quite short:

Maxwell's Equations, #1: nabla cdot D ~ = ~ %varrho_f

(Electric fields point away from positive electric charges, and towards negative ones.)
 Maxwell's Equations #2: nabla cdot B ~ = ~ 0

(There is no such thing as a magnetic charge.)
 Maxwell's Equations #3: nabla times E ~ = ~ - {alignc {partial B} over {partial t}}

(An electric field can be created by a changing magnetic field.)
 Maxwell's Equations #4: nabla times H ~ = ~ J_f + {partial D} over {partial t}

(A magnetic field can be created by a changing electric field or current.)

To most of you, none of that math made sense. There’s no shame in that; Maxwell used vector calculus to create those equations, which is rarely taught outside of a university. With the proper training, anyone could grasp them at a glance.

Wait. The elegance of those equations partially depends on your existing knowledge. While there aren’t a lot of symbols in those equations, each of them is rich in meaning. If you don’t know how to properly interpret them, Maxwell’s work is elegant in the way Kanji[89] is to  someone who doesn’t understand the language but likes its look.

On top of that, there are multiple ways to write those equations. The version I’ve used above is the free charge variant, in differential form. I chose it because it has fewer symbols than the other versions, and thus “looks” more elegant. You could unravel the shortcuts provided by vector calculus to make the underlying meaning more obvious, but that would result in an explosion of symbols. The written summaries I’ve cobbled together seem to accomplish elegance while providing meaning, but that’s only because I’ve massively simplified what each equation actually says!

If you want symbolic elegance, you must pay the cost of hidden meaning. There is no way to avoid it. On top of that, it’s easy to forget the cost once you’ve paid it. Thus the intellectual harmony that seems to pervade the universe is partially an illusion.

Dualism

Perhaps we’ve taken the wrong approach, however.

Maxwell accomplished his feat by taking observations about the universe and condensing them into a pithy intellectual description. We may have better luck in finding the underlying harmony if we do the reverse; instead of moving from the material to the intellectual, we should start with intellect and reason our way to the material universe.

Others have tried this. You’ve no doubt heard of the Pythagorean theorem, that states that the length of the longest side multiplied by itself equals the sum of the squares of the two remaining sides.[90] You probably know nothing about the Pythagoreans, however. That’s by design: they were an ancient Greek cult that kept quiet about most of their discoveries. From what little we can piece together, we know they worshipped numbers and believed that by contemplating them you could free yourself from continual reincarnation.

René Descartes took their ideas to the next level. This brilliant mathematician from the 17th century was also a deep philosopher, as mentioned in my section on the Ontological proof. It’s fitting that he coined the phrase “I think, therefore I am,” since he nearly lived by it. According to him, our senses frequently lie to us while thought is rarely wrong. The intellectual realm must be separate from the rest of reality, though it does have an influence through consciousness and physical laws.

This “dualism” rests on the assumptions that the universe of logic and math is more orderly than the material world, and that these two worlds are linked via consciousness. If consciousness really is a bridge to another world, one wonders where it is situated, fully in one world or somewhat split between the two. If it were mostly in the abstract, we’d expect it to be always available; this second universe is eternal and perfect, after all. And yet all humans shut off their consciousness for 6-10 hours every day via sleep. You could argue that dreams are a sort of continued consciousness, but that does little to save the argument. Dreams rarely last long, are less rich and notable than reality, freely defy logic, and only show up intermittently.

We also loose consciousness via anaesthetic just before surgery. While humans are somewhat aware of their surroundings while asleep, you can rip us to pieces if we’ve been chemically knocked out. The odds of having a dream are much lower, too. Consciousness is more tied to the physical world than the intellectual one.

Dualism also struggles with brain injury. If consciousness was somewhat separate from the physical world, you’d predict that physical trauma would have little to no effect. For example, if a blood vessel were to swell or burst in the brain, you’d expect the symptoms to be easily noticed and highly predictable.

Instead, strokes are difficult to diagnose. The most common symptoms are a weakness of the face or an arm, or difficulty speaking, but it’s also possible to have feelings of numbness, nausea or confusion; a loss of consciousness, vision, memory, or balance; a change in breathing or heart rate; or any of nearly a half-dozen more symptoms. Interestingly, the symptoms of a stroke are strongly linked to where the vessel burst.

More dramatic effects happen when a giant chuck of brain is removed entirely. Phineas Gage was compacting blasting powder and a fuse with a metal tamping rod, as part of the construction of a railway, when the powder accidentally exploded. The rod shot cleanly through his head, landing 25 metres behind him. Gage remained surprisingly alert, despite the new opening in his skull:

I first noticed the wound upon the head before I alighted from my carriage, the pulsations of the brain being very distinct. Mr. Gage, during the time I was examining this wound, was relating the manner in which he was injured to the bystanders. I did not believe Mr. Gage’s statement at that time, but thought he was deceived. Mr. Gage persisted in saying that the bar went through his head….Mr. G. got up and vomited; the effort of vomiting pressed out about half a teacupful of the brain, which fell upon the floor.

(Dr. Edward H. Williams, The American Journal of the Medical Sciences, July 1850)

Gage lived another twelve years, which was unheard of for a head injury that horrible. He was fit enough to work on a farm, and his only long-term problems were a partially paralysed face and no vision in his left eye.

Well, he did suffer from one more problem:[91]

The equilibrium or balance, so to speak, between his intellectual faculties and animal propensities, seems to have been destroyed. He is fitful, irreverent, indulging at times in the grossest profanity (which was not previously his custom), manifesting but little deference for his fellows, impatient of restraint or advice when it conflicts with his desires, at times pertinaciously obstinate, yet capricious and vacillating, devising many plans of future operations, which are no sooner arranged than they are abandoned in turn for others appearing more feasible. A child in his intellectual capacity and manifestations, he has the animal passions of a strong man. Previous to his injury, although untrained in the schools, he possessed a well-balanced mind, and was looked upon by those who knew him as a shrewd, smart businessman, very energetic and persistent in executing all his plans of operation. In this regard his mind was radically changed, so decidedly that hisfriends and acquaintances said he was “no longer Gage.”

(Dr. John Martyn Harlow, Bulletin of the Massachusetts Medical Society, 1868)

This was a sensation to contemporary psychologists. They had been debating whether or not changes to the brain could effect personality, and Gage’s case was the first chunk of evidence they couldn’t dismiss. Psychologists began collecting extensive case files on patients with brain trauma. These files did far more than link behaviour and personality to the physical brain; they allowed scientists to start mapping the brain, by matching a loss of functionality to a specific location.

Take HM.[92] He suffered from seizures since childhood, and by the time of his 16th birthday they would drop him to the floor with massive convulsions. The seizures came so often that he had to be institutionalized.  He was eventually placed in the care of Dr William Scoville, who tracked the source of the seizures to HM’s medial temporal lobes.[93] He proposed a radical therapy, the removal of both lobes.

The operation was a success, reducing the seizures from a crippling handicap into an occasional nuisance, but the loss of brain matter had an unexpected side effect: HM stopped forming new memories. Dr Scoville brought in a psychologist to help, Dr Brenda Milner. HM had to be reintroduced to her each time she walked into the room, even if she’d just left to graba drink, even a decade after she began working with him.

Remarkably, nothing else seemed wrong with HM. He did better on intelligence tests after the surgery, since he was on less medication. HM remembered his parents, childhood, and even some of his adult life normally, up to the two years before his surgery. He could easily carry on a conversation. He fell in love with crossword puzzles. Even his short term memory was fine, so he could remember a phone number or name for a bit. Other than some problems with grammar when he was reading, HM could pass as normal if you weren’t paying much attention.

HM had more surprises in store, however. Dr Milner asked him to do a complicated spacial task, which involved drawing stars through a mirror. He did poorly at first, but surprised her by getting better with practice! HM was no less shocked that he could ace a task he’d never seen before. He also wowed her by sketching the interior of his home from memory, even though he moved into it after the operation. Science had just discovered there were multiple kinds of long-term memory, each situated in different parts of the brain.

If this loss of memory was tied to a specific area, we’d expect similar problems in other patients with similar damage, and different problems in patients with different damage. That’s exactly what we find; Clive Wearing had the same area of his brain tampered with, this time thanks to a virus, and also can’t form new long-term memories. He’s famous for greeting
his wife as if she’s been gone for years when she’d last visited him ten minutes before, yet he can still conduct a choir. Gage had a different area ripped from his head, and so his long-term memory was intact.

In 1985, Anthony Barker developed a way to “fake” these injuries in otherwise healthy people. Trans-cranial Magnetic Stimulation sends a pulse of extremely powerful electric current into a coil of wire placed against the scalp. By carefully controlling this pulse, researchers can induce a smaller current in one part of the brain and disable it for a short while, all without cracking open the skull.

This technique can be used for all sorts of fun, from making someone’s arm jump to changing their morality. In the latter case, Rebecca Saxe and others at MIT gave their subjects a story like this:

Alice asks Bob to get her a coffee. As Bob fills the cup, he sees a container labelled “rat poison” and adds it to Alice’s drink. Fortunately it was just a mislabelled tin of sugar, so Alice was fine.

Half of them then had a region of the brain called the right temporo-parietal junction suppressed,[94] while the other half were zapped elsewhere. Both groups were asked immediately afterwards to rate how moral person B’s actions were. Those without a functional TPJ were more likely to say B acted morally than those with another area of their brain disabled.

 That was as expected: functional Magnetic Resonance Imaging had already suggested what that area of the brain did. The TPJ is where we ponder what something is thinking, what’s known as our “theory of mind.” Assessing the morality of this situation depends on being able to read person B’s intention; if you think they intended to kill A, then their actions were immoral.[95]

[89] The ornate Chinese characters that make up part of the Japanese alphabet, eg. 漢字

[90]  If you don’t think math is creative, search out proofs of the Pythagorian Theorem. There are hundreds to choose from, using every technique from high-level math to slicing up squares!

[91]  Gage’s psychological changes are somewhat controversial, since the evidence is thin and Harlow would sometimes exaggerate the change in personality. Recent evidence suggests Gage recovered most of his self-control before he died, though he was still a different person. Still, no-one denies he changed after the accident, they merely haggle over the degree of change.

[92]  To protect a patient’s identity, researchers refer to them only by their initials. HM has since passed away, and finally permitted his real name to be made public: Henry Gustav Molaison.

[93]  Incidentally, brain regions are named for where they are, not what they do. Take one of your hands and place the palm of it over one ear, thumb down, with your fingers wrapping around the back of your head, just above the spot where your neck attaches. You’re covering one of your temporal lobes; do the same with your other hand to cover the other. The medial bits are buried deep inside, right next to each other as well as the spot where your spine plugs in.

[94]  Remember the palm trick? First, find the bony bit of your right palm that’s just above your wrist. Now put your right palm to your right ear as before; that bit is roughly where the right TPJ is, right around where the top of your earlobe attaches to your head.

[95] Note that this also suggests a biological basis for Morality…

Everything Is Significant!

Back in 1939, Joseph Berkson made a bold statement.

I believe that an observant statistician who has had any considerable experience with applying the chi-square test repeatedly will agree with my statement that, as a matter of observation, when the numbers in the data are quite large, the P’s tend to come out small. Having observed this, and on reflection, I make the following dogmatic statement, referring for illustration to the normal curve: “If the normal curve is fitted to a body of data representing any real observations whatever of quantities in the physical world, then if the number of observations is extremely large—for instance, on an order of 200,000—the chi-square P will be small beyond any usual limit of significance.”

This dogmatic statement is made on the basis of an extrapolation of the observation referred to and can also be defended as a prediction from a priori considerations. For we may assume that it is practically certain that any series of real observations does not actually follow a normal curve with absolute exactitude in all respects, and no matter how small the discrepancy between the normal curve and the true curve of observations, the chi-square P will be small if the sample has a sufficiently large number of observations in it.

Berkson, Joseph. “Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test.” Journal of the American Statistical Association 33, no. 203 (1938): 526–536.
His prediction would be vindicated two decades later.

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