Math Can Be Weird

Take the Cantor function, a “Devil’s Staircase.”

The Cantor function, in the range [0:1]. It looks like a jagged staircase.

It looks like a squiggly mess, yet it is continuous and at almost every point there’s a well-defined slope: perfectly horizontal. The only exceptions are at points along the X-axis which are part of the Cantor set, an uncountable number of points with zero length. Even at one of these points, however, the net vertical increase is zero! We can see this by calculating the limits toward a point with a non-zero slope.

Wikipedia has a good write-up on how to evaluate the Cantor function (I used it in the above approximation).

  1. Express x in base 3.
  2. If x contains a 1, replace every digit after the first 1 by 0.
  3. Replace all 2s with 1s.
  4. Interpret the result as a binary number. The result is c(x).

The point x = 1/3 is part of the Cantor set, and thus satisfies our needs. Following the above rules, the output of the function there is 0.1 in binary, or 0.5 in decimal. Let’s calculate both limits, to get a feel for how much vertical is climbed at that point.

Approaching the limits of C(1/3). Spoiler alert, they both wind up equalling 1/2.

If we approach x = 1/3 from the right, we flatline at y = 1/2 . If  we approach it from the left, we wind up evaluating the geometric series y = 1/4 + 1/8 + 1/16 + … to calculate the height, which gets arbitrarily close to y = 1/2 . The height of the “jump” at x = 1/3 vanishes into insignificance! That’s a good thing, as otherwise the Cantor function’s slope would have approached a vertical line and it wouldn’t be a function.

Calculating the slope of the Cantor function at x = 1/3. Spoiler alert, it approaches a perfectly vertical slope.

Yet even though every single vertical hop is arbitrarily small, it’s obvious the Cantor function has some sort of vertical increase. How else could it contain both (0,0) and (1,1)?  In fact, if you measured the arc length of the Cantor function, it would be two units. Every point where the slope isn’t horizontal it is arbitrarily vertical, so no matter where you put the vertical or horizontal bits you wind up travelling the Manhattan distance between (0,0) and (1,1), which is 2. We know the distance of the horizontal components adds to one unit, since the Cantor set has length 0 and the horizontal distance is 1, so the uncountable number of arbitrarily small vertical “hops” must also have a net length of one unit.

The Cantor function manages to climb vertically without actually climbing vertically. Pretty wild, eh?

Oh, and credit where credit is due, I was introduced to the Cantor function by PBS’s Infinite Series. Check it out for a weekly dose of math.

Russian Hacking and Bayes’ Theorem, Part 2

I think I did a good job of laying out the core hypotheses last time, save two: the Iranian government or a disgruntled Democrat did it. I think I can pick them up on-the-fly, so let’s skip ahead to step 2.

The Priors

What’s the prior odds of the Kremlin hacking into the DNC and associated groups or people?
I’d say they’re pretty high. Right back to the Bolshevik revolution, Russian spy agencies have taken an interest in running disinformation campaigns. They have a word for gathering compromising information to blackmail people into doing their bidding, “kompromat.” Putin himself earned a favourable place in Boris Yeltsin’s government via some kompromat of one of Yeltsin’s opponents.
As for hacking elections, European intelligence agencies have also fingered Russia for using kompromat to interfere with elections in Germany, the Netherlands, Hungary, Georgia, and Ukraine.
That’s all well and good, but what about other actors? China also has sophisticated information warfare capabilities, but they seem more interested in trade secrets and tend to keep their discoveries under wraps. North Korea is a lot more splashy, but recently have focused on financial crimes. The Iranian government has apparently stepped up their online attack capabilities, and have a grudge against the USA, but apparently focus on infrastructure and disruption.
The DNC convention was rather contentious, with fans of Bernie Sanders bitter at how it turned out, and putting Trump in power had been preferred to voting for Clinton, for some, but it doesn’t fit the timeline: the DNC was suspicious of an attack in April, documents were leaked in June, but Sanders still had a chance of winning the nomination until the end of July.
An independent group is the real wild card, with any number of motivations and due to their lack of power eager to make it look like someone else did the deed.
What about the CIA or NSA? The latter claims to be just a passive listener, and I haven’t heard of anyone claiming otherwise. The CIA has a long history of interfering in other countries’ elections; in 1990’s Nicaragua, they even released documents to the media in order to smear a candidate they didn’t like. It’s one thing to muck around with other countries, however, as it’ll be nearly impossible for them to extradite you over for a proper trial. Muck around in your own country’s election, and there’s no shortage of reporters and prosecutors willing to go after you.
Where does all this get us? I’d say to a tier of prior likelihoods:
  • “The Kremlin did it” (A) and “Independent hackers did it” (D) have about the same prior.
  • “China,” (B) “North Korea,” (C) “Iran,” (H) and “the CIA” (E) are less likely than the prior two.
  • “the NSA” (F) and “disgruntled insider” (I) is less likely still.
  • And c’mon, I’m not nearly good enough to pull this off. (G)

The Evidence

I haven’t placed quantities to the priors, because the evidence side of things is pretty damning. Let’s take a specific example: the Cyrillic character set found in some of the leaked documents. We can both agree that this can be faked: switch around the keyboard layout, plant a few false names, and you’re done. Do it flawlessly and no-one will know otherwise.
But here’s the kicker: is there another hypothesis which is more likely than “the Kremlin did it,” on this bit of evidence? To focus on a specific case, is it more likely that an independent hacking group would leave Cyrillic characters and error messages in those documents than Russian hackers? This seems silly; an independent group could leave a false trail pointing to anyone, which dilutes the odds of them pointing the finger at a specific someone. Even if the independent group had a bias towards putting the blame on Russia, there’s still a chance they could finger someone else.
Put another way, a die numbered one through six could turn up a one when thrown, but a die with only ones on each face would be more likely to turn up a one. A one is always more likely from the second die. By the same token, even though it’s entirely plausible that an independent hacking group would switch their character sets, the evidence still provides better proof of Russian hacking.
What does evidence that points away from the Kremlin look like?

President Vladimir Putin says the Russian state has never been involved in hacking.

Speaking at a meeting with senior editors of leading international news agencies Thursday, Putin said that some individual “patriotic” hackers could mount some attacks amid the current cold spell in Russia’s relations with the West.
But he categorically insisted that “we don’t engage in that at the state level.”

Is this great evidence? Hell no, it’s entirely possible Putin is lying, and given the history of KGB and FSB it’s probable. But all that does is blunt the magnitude of the likelihoods, it doesn’t change their direction. By the same token, this ….
Intelligence agency leaders repeated their determination Thursday that only “the senior most officials” in Russia could have authorized recent hacks into Democratic National Committee and Clinton officials’ emails during the presidential election.
Director of National Intelligence James Clapper affirmed an Oct. 7 joint statement from 17 intelligence agencies that the Russian government directed the election interference…
….  counts as evidence in favour of the Kremlin being the culprit, even if you think James Clapper is a dirty rotten liar. Again, we can quibble over how much it shifts the balance, but no other hypothesis is more favoured by it.
We can carry on like this through a lot of the other evidence.
I can’t find anyone who’s suggested North Korea or the NSA did it. The consensus seems to point towards the Kremlin, and while there are scattered bits of evidence pointing elsewhere there isn’t a lot of credibility or analysis attached, and some of it is “anyone but Russia” instead of “group X,” which softens the gains made by other hypotheses.
The net result is that the already-strong priors for “the Kremlin did it” combine with the direction the evidence points in, and favour that hypothesis even more. How strongly it favours that hypothesis depends on how you weight the evidence, but you have to do some wild contortions to put another hypothesis ahead of it. A qualitative analysis is all we need.
Now, to some people this isn’t good enough. I’ve got two objections to deal with, one from Sam Biddle over at The Intercept, and another from Marcus Ranum at stderr. Part three, anyone?

A Third One!

I know, I know, these are starting to get passé. But this third event brings a little more information.

For the third time in a year and a half, the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO) has detected gravitational waves. […]

This most recent event, which we detected on Jan. 4, 2017, is the most distant source we’ve observed so far. Because gravitational waves travel at the speed of light, when we look at very distant objects, we also look back in time. This most recent event is also the most ancient gravitational wave source we’ve detected so far, having occurred over two billion years ago. Back then, the universe itself was 20 percent smaller than it is today, and multicellular life had not yet arisen on Earth.

The mass of the final black hole left behind after this most recent collision is 50 times the mass of our sun. Prior to the first detected event, which weighed in at 60 times the mass of the sun, astronomers didn’t think such massive black holes could be formed in this way. While the second event was only 20 solar masses, detecting this additional very massive event suggests that such systems not only exist, but may be relatively common.

Thanks to this third event, astronomers can set a stronger maximum mass for the graviton, the proposed name for any gravity force-carrying particle. They also have some hints as to how these black holes form; the axis of spin for these two black holes appear to be misaligned, which suggests they became binaries well after forming as opposed to starting off as binary stars in orbit. Finally, the absence of another signal tells us something important about intermediate black holes, thousands of times heavier than the Sun but less than millions.

The paper reports a “survey of the universe for midsize-black-hole collisions up to 5 billion light years ago,” says Karan Jani, a former Georgia Tech Ph.D. physics student who participated in the study. That volume of space contains about 100 million galaxies the size of the Milky Way. Nowhere in that space did the study find a collision of midsize black holes.

“Clearly they are much, much rarer than low-mass black holes, three collisions of which LIGO has detected so far,” Jani says. Nevertheless, should a gravitational wave from two Goldilocks black holes colliding ever gets detected, Jani adds, “we have all the tools to dissect the signal.”

If you want more info, Veritasium has a quick summary, while if you want something meatier the full paper has been published and the raw data has been released.

Otherwise, just be content that we’ve learned a little more about the world.

The Monkey’s Climate Agreement

This must have seemed like an excellent idea to Trump.

I am fighting every day for the great people of this country. Therefore, in order to fulfill my solemn duty to protect America and its citizens, the United States will withdraw from the Paris Climate Accord.


Thank you. Thank you.

But begin negotiations to re-enter, either the Paris Accord or in, really entirely new transaction on terms that are fair to the United States, its businesses, its workers, its people, its taxpayers. So we’re getting out. But will we start to negotiate and we will see if we can make a deal that’s fair. And if we can, that’s great. And if we can’t, that’s fine.

It distracts from the ongoing Russia scandal, and it’s a move which will earn favour from many Republicans. But there’s also good reason to think it won’t have the effect Trump hopes for.

For one, the USA has been very successful at watering down past climate agreements.

When aggressively lobbying to weaken the Paris accord, U.S. negotiators usually argued that anything stronger would be blocked by the Republican-controlled House and Senate. And that was probably true. But some of the weakening — particularly those measures focused on equity between rich and poor nations — was pursued mainly out of habit, because looking after U.S. corporate interests is what the United States does in international negotiations.

Whatever the reasons, the end result was an agreement that has a decent temperature target, and an excruciatingly weak and half-assed plan for reaching it.

If the US withdraws from climate talks, as seems likely despite Trump’s “renegotiation” line, the US delegation won’t be at the table. And with China now in full support of taking action, India pushing for aggressive targets, and even Canada still willing to stick with the Paris agreement, there’s no one left to step on the brakes. Future climate change agreements will be more aggressive.

They might also carry penalties for non-signing nations. There are only three countries who didn’t sign the Paris agreement: Nicaragua didn’t sign because the agreement didn’t go far enough, Syria had been diplomatically isolated so they weren’t even invited to the table, and the US refused to even submit it for ratification by Congress. Yes, the US is a major player in world financial markets, but its dwarfed by the output of the rest of the world. If the globe agreed to impose a carbon tax on non-signing nations, the US could do little to push back.

Even if the rest of the world doesn’t have the appetite for that route, there are more creative kinds of penalties.

Calling the President’s decision “a mistake” for the US as well as the planet, [French President] Macron urged climate change scientists, engineers and entrepreneurs to go to France to continue their work. “They will find in France a second homeland,” Mr Macron said. “I call on them,” he added. “Come and work here with us, work together on concrete solutions for our climate, our environment. I can assure you, France will not give up the fight.”

Climate change has become the one thing the international community could reach a consensus on. Pulling from the Paris agreement was like kicking a puppy; regardless of the intent or circumstances, it’s an action the world can unite against. It makes for a convenient excuse to isolate the US or play hardball, much more so than any boorish behaviour by Trump.

It also won’t stop the US from following the Paris agreement anyway.

Representatives of American cities, states and companies are preparing to submit a plan to the United Nations pledging to meet the United States’ greenhouse gas emissions targets under the Paris climate accord, despite President Trump’s decision to withdraw from the agreement.

The unnamed group — which, so far, includes 30 mayors, three governors, more than 80 university presidents and more than 100 businesses — is negotiating with the United Nations to have its submission accepted alongside contributions to the Paris climate deal by other nations.

“We’re going to do everything America would have done if it had stayed committed,” Michael Bloomberg, the former New York City mayor who is coordinating the effort, said in an interview. […]

“The electric jolt of the last 48 hours is accelerating this process that was already underway,” said Mr. Orr, who is now dean of the School of Public Policy at the University of Maryland. “It’s not just the volume of actors that is increasing, it’s that they are starting to coordinate in a much more integral way.”

Various US states, municipalities, universities, businesses, and even the military have been working towards cutting emissions for years without waiting for the federal government to get its act in order. A national policy would be more effective, but these piecemeal efforts have substantial force behind them and look to be gaining even more.

Finally, the boost this move earns from his supporters may get cancelled out by backlash from everyone else.

It’s also possible that Trump gave a win to his base on an issue they don’t care that much about while angering the opposition on an issue they do care about. Gallup and Pew Research Center polls indicate that global warming and fighting climate change have become higher priorities for Democrats over the past year. … As we wrote earlier, if Trump’s voters view the Paris withdrawal as an economic move, he’ll likely reap some political benefit from it. If, however, it’s viewed as mostly having to do with climate change, perhaps Trump won’t see much gain with his base. Jobs, the economy and health care rate as top issues for Republicans, but climate change and the environment do not, so it’s hard to know how Trump voters would weigh the president doing something they don’t like on an issue they care a lot about (the GOP health care bill) against him doing something they do like on an issue they don’t care much about (withdrawing from Paris).

This may have looked like an easy win for Trump, but the reality could be anything from a weak victory to a solid defeat. Time will tell, as it always does.

Proof from Transcendence (2)


No doubt, this seems like I’m stretching. How can spiritual transcendence be the same as the non-spiritual kind? The two seem very different.

In the past two decades, a new term has sprung up: neurotheology. Scientists armed with brain scanners have begun using them on the devout, looking for any interesting patterns. Unfortunately, most approach this from the theological side, either taking the existence of a god as fact or explicitly stating they are uninterested in its existence. This tends to colour their interpretations of the data.

Still, there are interesting nuggets to be found. For instance, Andrew Newberg has compared the minds of believers while they meditated to those of atheists doing the same thing, and found no difference between the two. In study after study, this pattern holds:

When we look at how the brain works, it has a limited set of functions. So if one has a feeling of euphoria — whether one gets that through sex or religion or watching your team win the championship — it’s probably going to activate similar areas of the brain. There’s a continuum of these experiences. […]

Are we really capturing something that’s inherently spiritual? This is a big philosophical question. If the soul or the spirit is really non-material, how does it interact with us? Of course, the human brain has to have some way of thinking about it. Perhaps the most interesting finding I could have would be to see nothing change on the brain scan when one of the nuns has an incredible experience of transcendence and connectedness with God. Maybe then we really would capture something that’s spiritual rather than just cognitive and biological.

(Andrew Newberg, interviewed by Steve Paulson for Salon. Sept 20, 2006. )

If there were some legitimate difference between believers and non-believers, we’d expect some difference in the brain itself. Instead, it seems that behaviour is far more influential than belief; by merely repeating the same actions, we see the same patterns across both categories.

Note that this is not disproof against a god by itself. Others have used the very same observations to claim that everyone has a spiritual connection, even those that don’t believe in it. This is a valid interpretation, but it doesn’t line up with the claims of believers. People who don’t believe or are in the wrong religion are fundamentally different from those in the right religion, since only the last has true contact with the real god or gods. We should see this difference reflected somewhere. Secondly, it depends on the existence of a god to make sense. This is a problem, since the alternate explanation does not depend on the existence any god, it only discounts that the brain has a special channel to the gods, but the theory is otherwise agnostic about them. We can begin sharpening Ockham’s Razor.

But first, there’s more evidence to ponder. The Pentecostals, a Christian sect, believe that “speaking in tongues” is the highest form of worship. Also known as glossolalia, it’s a sort of spoken gibberish, sometimes while writhing around on the floor, and is claimed to be the sign of God speaking through those people. This makes an interesting test case, since both prayer and glossolalia attempt to contact the same god through different behaviours. If both have the same brain activation patterns, this would be clear proof that a deity was involved; if the brain and body were material things, different external behaviour must correspond to a different internal state.

Newberg’s studies show that the brain states are different. He’s catalogued the regions of the brain involved in both activities:

  • thalamus: linked to processing the senses. More active than usual in both prayer and glossolalia.
  • temporal lobes: linked to processing our emotions. More active in both.
  • frontal lobe:[167] linked to our ability to concentrate and focus. More active in prayer, but inactive in glossolalia.
  • parietal lobe: linked to feelings of self, and how it relates to the world. Less active in prayer, no effect during glossolalia.

Interesting, isn’t it? When people pray, they focus on losing their sense of self and the external world, feeling an emotional lift they think is a real experience; at the same time, the corresponding areas of the brain fire up or shut down, according to need. Meditation has roughly the same effect, and roughly the same brain patterns. When people speak in tongues, losing their focus (but not their sense of self) to an emotional lift that feels very real, the brain also changes accordingly. The areas of their brain responsible for language do not light up, and linguists studying the sounds uttered during glossolalia can find no evidence of linguistic structure. Note that every activated region is not reserved for religious use, but one that we discovered being used by some secular activity.

This pattern is exactly what we’d expect if the brain was purely material, and the feelings attributed to religion were just existing ones put to a different use. This pattern is not what we’d expect if a divine being were beaming those feelings directly into our minds.

Still, this is not a dis-proof of the gods; I can find no studies that checked if the feelings of transcendence came before the brain activity, for instance, which could have provided evidence for the theist side. It’s quite possible that a god grants us these feelings by tugging on the appropriate portions of the brain. On the other hand, if we said this pattern were the actions of a god we’d be assuming a god existed, while if we claimed it was purely material we’d make no such assumption. Ockham’s Razor says we should go with the material theory, rendering the gods irrelevant yet again.

Precision from the Non-Precise

There’s an odd hypocrisy to this proof.

Have a careful look at the two squares, and tell me which one is lighter:Adelson's checker shadow illusion.

Sorry, that was a trick question: both squares have the same tone.

Are you feeling any anger at your senses? I doubt it, we’re happy to admit they lead us astray. That goes doubly so for the religious, because it allows them to dismiss a lack of physical evidence and invoke the Transcendence Proof.

[FUTURE HJH: I left this bit incomplete. My basic plan was to link to Descarte’s invocation of God as a fundamental belief. This website provides a basic sketch.]

Why, though, are we so content to accept this inaccuracy? We rely on our senses to an astonishing degree, after all. I think it’s a safe assumption that you’re absorbing this text through your senses. Was any part of it blocked by a malfunctioning sense? Did you have to repeat certain passages, because the words kept changing on you? Did the page suddenly zip away or flip upside down? Think of all the possible moments, and all the possible ways, this text could have been screwed up by your senses, and total up how many of them have happened so far. For most people, I’m sure, that total is comfortably close to zero.

Now total up the number of moments that went right. Are they near zero? Or substantially higher?

Let’s say you’re one of the unlucky few. Pretend that on average, one out of every ten words you absorb were not written by me. Does that make this book unreadable? Certainly not. If you scan each passage twice, the odds of a word being wrong both times drop are one in a hundred. Three readings pushes the odds down to one in a thousand, and the more readings you’re willing to do, the more confident you can be that you’re reading what I wrote.

What if we don’t know the odds? Fortunately, the English language has roughly 200,000 words, so there are far more ways to be wrong than right. The odds of the same wrong word being picked twice in a row are roughly one in 200,000, so if you read the same word twice you can be quite confident it’s the right one. Switching to a language with a ridiculously small vocabulary still doesn’t stop you from moving forward, it just requires more scanning.

We don’t fret over unreliable senses because it’s trivially easy to make them reliable enough. Consider the colour puzzle; in that case, multiple samples will never lead you to conclude both squares are the same shade. However a simple mask, cut out of paper, will quickly make the truth obvious. When you start to employ multiple senses, and use or augment them in multiple ways, you can be quite sure they haven’t led you astray.

What about our feelings, though? Can they be fooled, like our other senses? It would be very odd to claim that easily verified senses like vision are unreliable, and yet fuzzy, non-specific feelings are perfectly reliable.

If they can steer us the wrong way, then how can we trust them without putting them to the test? How can we rely on them to tell the truth, without looking for and ruling out alternate explanations first?

[167]  From one ear, draw around the front of your head at eyebrow-level to the other ear, then return by going over the very top of your head. You’ve just outlined the boundaries of your frontal lobes.

Russian Hacking and Bayes’ Theorem, Part 1

I’m a bit of an oddity on this network, as I’m pretty convinced Russia was behind the DNC email hack. I know both Mano Singham and Marcus Ranum suspect someone else is responsible, last I checked, and Myers might lean that way too. Looking around, though, I don’t think anyone’s made the case in favor of Russian hacking. I might as well use it as an excuse to walk everyone through using Bayes’ Theorem in an informal setting.

(Spoiler alert: it’s the exact same method we’d use in a formal setting, but with more approximations and qualitative responses.)

[Read more…]

Proof from Transcendence (1)

In the span of your life, you’ve probably experienced a lot of highs and lows. Sometimes, things are going so well that you completely forget yourself; sometimes, things are so bad that you are desperate for any sort of help.

Did you ever stop to think where those feelings were coming from? Perhaps they are little hints from a deity, wee stone markers placed on a giant mountain that whisper “I’m here.” Just like a pebble hitting the top of an unsteady slope, these little nudges could trigger much greater changes within you. Maybe it can pick you up when you’re down, or even save your life:

Travis Barker’s ex-wife, Shanna Moakler, told US Weekly that she was supposed to be aboard the private jet that crashed in South Carolina on September 19, injuring Barker and DJ AM and killing four others, but she changed her plans at the last minute because she had “a bad feeling.”

“I was supposed to go with [Travis] to South Carolina, and at the last minute, I had this gnarly feeling and said, ‘I don’t think we should fly together anymore,’ ” she told the magazine in its October 17 issue, which hits stands Friday. “God forbid something ever happened … our kids wouldn’t have both parents. Instead of flying a commercial flight back home, they decided to take a private jet. He e-mailed me pictures of the plane and wrote, ‘It’s really small and scary.’ I had a bad feeling, but didn’t want to sound strange, so I said, ‘Be safe.’ “

(a news article for, by James Montgomery, dated October 16th, 2008.  )

It could explain why we’re so curious about deities. What if we all have a concept of the gods built into us, one that will only bubble up if we let it?

The most frequently mentioned barrier to a personal relationship with God is never having experienced God’s presence. “If only I felt something,” some Catholics have told me, “then it would be easier to pray.” “If only God made his presence known,” say seekers, “then I could start down the path of faith.” Even agnostics like my friend-as well as atheists-seeking intellectual proofs for God’s existence admit that if they saw a glimmer of God, maybe they’d consider believing.

(“More than a feeling: A desire for God,” by James Martin. U.S. Catholic, July 2010, Vol. 75, No. 7)

Older than Dirt

I suspect this proof is one of the oldest, if not the first. For one, it doesn’t need any sort of logic or language to make. Simply feeling a wonderful feeling is enough, and we have every reason to think emotions pre-date human beings. Fear, for instance, has been linked to our thalamus, one of the most “primitive” portions of the brain.[164] Paul Ekman has found that some facial expressions, our external signal of emotion, are nearly universal across all human cultures and thus likely pre-date humans.[165]

For two, we know human beings have been searching for feelings of transcendence for some time. Some tribes of North America sent their children on a vision quest, which usually consists of a multi-day fast and constant meditation in the wilderness, sometimes helped along by narcotics or sleep deprivation. The goal is to find their life’s purpose via the spirit world. Some people experienced actual visions, complete with a guardian animal; others just got a feeling of transcendence. The Bhagavad Gītā, a key holy text of the Hindu religion, discusses transcendence at some length.

[When] the yogī engages himself with sincere endeavor in making further progress, being washed of all contaminations, then ultimately, achieving perfection after many, many births of practice, he attains the supreme goal.

A yogī is greater than the ascetic, greater than the empiricist and greater than the fruitive worker. Therefore, O Arjuna, in all circumstances, be a yogī.

And of all yogīs, the one with great faith who always abides in Me, thinks of Me within himself, and renders transcendental loving service to Me — he is the most intimately united with Me in yoga and is the highest of all. That is My opinion.

(Chapters 6.40-6.47, translated by A. C. Bhaktivedanta Swami Prabhupada)

Notice that both accounts describe much more than feelings, though. Krishna is also talking about his Vishvarupa, or “Universal Form:”

Arjuna saw in that universal form unlimited mouths and unlimited eyes. It was all wondrous. The form was decorated with divine, dazzling ornaments and arrayed in many garbs. He was garlanded gloriously, and there were many scents smeared over His body. All was magnificent, all-expanding, unlimited. This was seen by Arjuna.

If hundreds of thousands of suns rose up at once into the sky, they might resemble the effulgence of the Supreme Person in that universal form.

At that time Arjuna could see in the universal form of the Lord the unlimited expansions of the universe situated in one place although divided into many, many thousands.

Then, bewildered and astonished, his hair standing on end, Arjuna began to pray with folded hands, offering obeisances to the Supreme Lord.

Arjuna said: My dear Lord Krishna, I see assembled together in Your body all the demigods and various other living entities. I see Brahmā sitting on the lotus flower as well as Lord Śiva and many sages and divine serpents.

(Chapters 11.10-11.16, translated by A. C. Bhaktivedanta Swami Prabhupada)

 That sounds suspiciously like proof by Witness. Prayers can also bring feelings of transcendence, yet are frequently tied to proof by Miracle as well:

Although everyone was puzzled about my condition, even me, I knew that the one thing for sure was that God, my Lord and savior was in control of my life. As I laid there in that hospital bed day and night, I prayed, meditated and spoke to God reflecting on my life, trials and tribulations.I believe I had an out of body experience with a peaceful bright light pure moment. I made up in my mind that I was going to let go and let God! I started making peace and preparation mentally to God that if it was my time to go in his plan, I will trust him.

That being said, I knew my life had purpose and that he wasn’t through with me yet. When I let God have total control, I started to make progress and improve. Giving God high praise for His grace and mercy for me. All the prayers from family, friends the medical staff and complete strangers helped throughout this ordeal.

I don’t know why I suddenly became so ill that year, and doctors not giving me a diagnosis, but I trust God’s plan because I never would have made it without him and his son Jesus! There’s a saying that “God works in mysterious ways and he’s a miracle worker”. I know because I’m a living testimonial miracle, thank you God, thank you Jesus!

(“C.R.” from Tennessee, retrieved June 6th 2011)

To clear up this tangle, I’ve set up borders around each proof:

  • Miracle proof: A deity makes a change to the universe for multiple people, directly through the senses.
  • Witness proof: A deity makes a change to the universe for one person, directly or indirectly through the senses.
  • Transcendence: A deity changes a person without involving the senses.

By the above definitions, “hearing voices” or “seeing visions” is the domain of the Witness proof, even if the person experiencing them claims they were entirely internal. I don’t limit the senses to the traditional five, either, so your ability to sense how your limbs are positioned or how hungry you are count just as much.

That doesn’t leave a lot left for Transcendence. We have logic, our method for exploring the external world and our internals via conscious effort, and emotions, which are a representation our internal unconscious state. The first part’s already been covered by the Logic proof, which leaves us to consider emotions.

Hooked on a Feeling

Emotions are… a lot of things.

They can bring us to action. For seven weeks in 1904, Upton Sinclair took several jobs at meatpacking plants. He wanted to write a novel that would explore the plight of new immigrants, by showing the harsh conditions they were forced to work under. Sinclair filled the book with vivid tales of con men and corruption, but it was the descriptions of those meatpacking plants that caught the public’s imagination. Bowing to the public’s feeling of disgust, the U.S. Government and Teddy Roosevelt passed the “Meat Inspection” and “Pure Food and Drug” Acts, which began regulating the food industry.

Emotions can paralyse us. Depression is a persistent feeling of sadness, by far the most common psychological problem in humans. Most of us will go through it at some point in our lives, and feel a little of its paralytic sting. An unlucky few have it to such an extreme that their paralysis is almost literal; they rarely get out of bed, spend most of the day sleeping, and need to be taken care of by others.

Emotions are somewhat independent of conscious thought. The brain structures are in quite different places, and the key emotional centres are close to the brain stem and other ancient structures. This makes a lot of sense: not all food is created equal, for instance. Fats contain more calories per unit than sugars. An organism that was better at seeking out fat would do better than one that did not in the long term. An organism that was given a reward for eating fat might do better still. And a happy feeling certainly counts as a reward.

Similar reasoning applies to running. A little while ago, we only ran to escape being eaten or to catch food. Afterwards, our bodies would begin to repair any damage received. As part of the process, it would dull the sensation of pain and inadvertently give us another high. Not only would that encourage us to run again in future, but we’d be far more likely to run while playing with others. This “exercise” would prepare them for a future encounter, increasing their odds of survival.

Having said that, consciousness can exert some control over emotion. In modern times, humans usually run for “fun.” More accurately, our reasons to exercise aren’t directly linked to survival; we jog to look more attractive to the opposite sex, or for the social atmosphere a group provides, or to enjoy the challenge of training, or to take advantage of the feelings exercise triggers within us. Exercising has become a more conscious decision, yet the boost to our mood remains.

We also control our feelings more directly. Cognitive behaviour theory holds that your thoughts about the world effect your emotions. By challenging the negative views you hold and substituting neutral or positive ones instead, CBT claims it can cure mild to moderate depression. The science seems to back that up; CBT is the most successful verbal therapy in the psychologist’s toolkit, and out-performs most medicine- or surgery-based therapies.[166]

I would place more credence in the transcendence argument if the only people who experienced it were from a specific religion. This isn’t the case; Jains and Buddhists both feel that divine touch, for instance. In particular, Jainism does not attribute that to a god, instead claiming it as proof that someone is getting in “touch” with the universe. I myself have experienced this feeling several times, and in each case it’s been triggered by the material world, with no sign of divine prompting.

So how can something that is normally linked to a god also appear in the god-less? It must be caused by something other than a deity.

Suppose you have a group of people chanting passionately and enjoying themselves. Human beings are social critters, so we try to read what other people are thinking. We’re hoping to exploit this, either directly by lying or indirectly by forging closer ties that might save our bacon later. Mirroring other people is a good way to get close to someone, since it shows they’re not alone. If they appear sad, we feel sad; if they’re happy, we feel happy as well. It also saves precious brain resources, by allowing some cells to do double-duty and respond to other’s emotions as well as our own.

If you’re within this group, then, their emotions will have a strong influence on your emotions. Lacking a connection to someone could lead you into conflict, in the worst case; having a conflict with a group can be somewhat unhealthy! So if there’s a state of euphoria or transcendence in the air, you’ll pick it up. The entire process is so basic that it’s been built into us by evolution, and is largely unconscious and automatic.

Now suppose you’ve been told those feelings are due to a god. Because this process is automatic, you might not realize why those feelings are bubbling up in the first place. Feelings are primitive, older than rational thought, so you can’t easily use the other to examine the one. With no clear cause to be found, it would be easy to convince yourself those feelings are due to a deity. If the god-transcendence connection is hammered into your head repeatedly, you become conditioned to think it automatically, to the point where you can consciously trigger those feelings by thinking of the deity.

And so, a desire for pleasure becomes a desire for pleasure through the gods.

[You] feel lifted up, or likewise, a sense of exaltation or happiness. Different from longing to know what it’s all about, you feel that you are very close to, or are about to meet, the object of your desire. You may even feel the warmth of being near God, though you may be reluctant or embarrassed to define it as such.

Each of these feelings, by the way, may overlap. And there’s no need to identify them precisely. Sometimes the feelings that are the most difficult to describe are those that are the most personal, the most tailored to your own situation. Here God may be speaking more clearly than anywhere else. Just because you can’t describe it doesn’t mean it’s not real.

(“More than a feeling: A desire for God,” by James Martin. U.S. Catholic, July 2010, Vol. 75, No. 7)

Likewise, a desire for learning becomes a desire for learning about a god.

A desire for fulfilment becomes a desire for fulfilment with gods.

A desire for security becomes a desire for security within the god.

Suppose instead this chanting group was at a concert or party. Again you’d feel transcendent, but the blame for that would fall elsewhere. It might transfer to the band, making you a fan. Listening to a recording of their work, or even thinking about that night would bring back those feelings. It might transfer to the friends by your side, which would strengthen your social ties further. It might get associated with what you’re drinking, or parties in general. Or it might be a combination of these, or none of them.

Those feelings have a non-spiritual origin, but can be associated with spirituality or anything else you like. Adding the supernatural does not change those feelings in any way, nor does it offer proof of the supernatural.

Because feelings are just another sense, only about your internal state instead of the external world. The fact that you can’t point to what triggered your sensation, unlike most other senses, doesn’t rule out a natural explanation.

[164]  Picture your brain as a lollipop, with your spine as the stick. The thalamus is right at the top of that stick, deep within the brain. We call it “primitive” because it’s in nearly every animal with a spine, so it must have evolved early in order to be so widespread.

[165]  “Constants across cultures in the face and emotion,” Paul Ekman, Wallace Friesen. Journal of Personality and Social Psychology 17 (2), 1971.

[166]  Antidepressant drugs, long thought to be about as effective as CBT, have been called into question for mild-to-moderate depression recently; for one example, see “Antidepressant Drug Effects and Depression Severity,” Jay C. Fournier et al, JAMA. 2010; 303(1):47-53. Electroconvulsive or shock therapy is on a comeback, but only for the most severe cases. Transcranial magnetic stimulation is used when shock therapy fails.

Journal Club 1: Gender Studies

Last time, I pointed out that within the Boghossian/Lindsay kerfuffle no-one was explaining how you could falsify gender studies. As I’ve read more and more of those criticisms, I’ve noticed another omission: what the heck is in a gender studies journal? The original paper only makes sense if it closely mirrors what you’d find in a relevant journal.

So let’s abuse my academic access to pop open the cover of one such journal.

Gender & Society, the official journal of Sociologists for Women in Society, is a top-ranked journal in sociology and women’s studies and publishes less than 10% of all papers submitted to it. Articles analyze gender and gendered processes in interactions, organizations, societies, and global and transnational spaces. The journal publishes empirical articles, along with reviews of books.

They also happened to be at the top of one list of gender studies journals. I’ll go with their latest edition as of this typing, volume 31 issue 3, which is dated June 2017.

[Read more…]

Proof from Fine-Tuning (2)

Do Androids Dream of Anthropic Sheep?

I doubt that will feel like a satisfying answer. Even if the universe is not perfect for us, the fact that we’re even here seems too good to be true. Isn’t it more likely that unintelligent life should be here instead of us? Why is there something instead of nothing?

I think I can answer that through a series of questions.

What would this universe look like if it was inhospitable to life? This is clear nonsense, since there’d be no life around to ask the question, let alone answer it. We can use our theories of the universe to guess, but as pointed out above we’d need to assume they can be tuned, guess what settings we could change, and then via some assumptions rank their friendliness to life. This leads to an important point: life can only bloom in a universe that is compatible for life, and only life can ask questions.

What would this universe look like if it didn’t allow intelligent life? This is an equally silly question, for the same reasons. Because we can ask it at all, our universe must be compatible with intelligent life.

Time for a tricky one: How can we tell a compatible universe from a tuned one? If we’re lucky, the answer will be buried in either the initial state or the laws of the universe. If not, we could check if we’re in the best possible universe, and argue that’s unlikely to happen by chance. Failing that, we’ll have to tally up the tunings better than ours, calculate the odds of our particular tuning, and decide if it’s sufficiently unlikely to happen by chance.

In all three cases, we’re not only dependent on the missing information I pointed out earlier, we may need to add more, like the odds of a specific tuning happening. Worst of all, in one case we’re forced to consider when we transition from “unlikely to happen by chance” to “impossible to happen.” Even if the odds were a million to one against something happening, it could still happen by chance. It’s like a lottery winner claiming they were destined to win the lottery, because the odds of anyone winning the lottery are so low that no-one should have been able to win it.

Faced with so many unanswered questions in the way, both believers and unbelievers have simply made up answers to the compatibility problem. And when the answers are invented, the conclusion is predictable:

Design advocates argue that the universe seems to have been specifically designed so that intelligent life would form. These claims are essentially a modern, cosmological version of the ancient argument from design for the existence of God. However, the new version is as deeply flawed as its predecessors, making many unjustified assumptions and being inconsistent with existing knowledge. One gross and fatal assumption is that only one kind of life, ours, is conceivable in every conceivable configuration of universes.

However, a wide variation of constants of physics leads to universes that are long-lived enough for life to evolve, although human life need not exist in such universes.

(“IS THE UNIVERSE FINE-TUNED FOR US? ”, Victor J. Stenger , Emeritus Professor of Physics, University of Hawaii)

Stenger attempts to show that our universe isn’t really fine-tuned by showing that long-lived stars are not unusual. He fails for five reasons. 1.) He gets his formula wrong, and in so doing ignores an important case of fine-tuning. 2.) He fails to consider the effect of altering the strength of gravity. 3.) He “cherry-picks” a very favourable fine-tuning example to suit his purposes. 4.) His probability claims are vacuous, following trivially from his unjustified hidden assumptions. 5.) He rightly exhorts us to consider varying multiple parameters at once, but commits the opposite mistake: he fails to consider multiple life-permitting criteria. Even if he were right about long-lived stars, it doesn’t follow that life-permitting universes do not need to be fine-tuned. I conclude that Stenger’s claims are worse than mistaken; they are misleading.

(“No Faith In MonkeyGod: A Fine-Tuned Critique of Victor Stenger (Part 2),” Luke Barnes, Postgraduate Researcher at the Institute for Astronomy at ETH Zurich, in Letters to Nature, April 18, 2010)

A compatible universe can look like a tuned one, if you invent the proper answers. Refuse to do so, and all you can conclude is that the universe is compatible with intelligent life, because intelligent life exists.[163]

Carts and Horses, Meet Cranes and Skyhooks

There’s one more assumption floating around behind this pseudo-proof: the universe is tuned for life.

Is that really the case, though? In the Design proof, I discuss evolution and how it works. Specifically, I pointed out that the products of evolution are tuned to the environment around them by the environment itself. Life, from all indications, is a product of evolution.

Thus, life tuned itself to the universe, and not the other way around. This explains why the two seem unusually compatible: life has adjusted to the challenges thrown down by the universe, altering itself appropriately. If it had not, you wouldn’t be around to ask why the two seem so compatible.

Douglas Adams compared the Fine Tuning pseudo-proof to a puddle:

It’s rather is if you imagine a puddle, waking up one morning and thinking hmm this is an interesting world I find myself in, an interesting hole I find myself in, it fits me rather neatly, doesn’t it. In fact it fits me staggeringly well, must have been made to have me in it!

This is such a powerful idea that as the sun rises in the sky and the air heats up and, as gradually the puddle gets smaller and smaller it’s still frantically hanging onto the notion that everything’s going to be all right because this world was meant to have him in it, was built to have him in it. So the moment he disappears catches him rather by surprise. I think this maybe something we need to be on the watch for.

Indeed, lest we push a proof that isn’t one at all.

[163]  Notwithstanding the old astronomy joke about searching for intelligent life in the universe.

About Damn Time

Ask me to name the graph that annoys me the most, and I’ll point to this one.538's graph of Trump's popularity, as of May 25th, 2017.

Yes, Trump entered his presidency as the least liked in modern history, but he’s repeatedly interfered with Russian-related investigations and admitted he did it to save his butt. That’s a Watergate-level scandal, yet his approval numbers have barely changed. He’s also pushed a much-hated healthcare reform bill, been defeated multiple times in court, tried to inch away from his wall pledge, and in general repeatedly angered his base. His approval ratings should be negative by now, but because the US is so polarized many conservatives are clinging to him anyway.

A widely held tenet of the current conventional wisdom is that while President Trump might not be popular overall, he has a high floor on his support. Trump’s sizable and enthusiastic base — perhaps 35 to 40 percent of the country — won’t abandon him any time soon, the theory goes, and they don’t necessarily care about some of the controversies that the “mainstream media” treats as game-changing developments. […]

But the theory isn’t supported by the evidence. To the contrary, Trump’s base seems to be eroding. There’s been a considerable decline in the number of Americans who strongly approve of Trump, from a peak of around 30 percent in February to just 21 or 22 percent of the electorate now. (The decline in Trump’s strong approval ratings is larger than the overall decline in his approval ratings, in fact.) Far from having unconditional love from his base, Trump has already lost almost a third of his strong support. And voters who strongly disapprove of Trump outnumber those who strongly approve of him by about a 2-to-1 ratio, which could presage an “enthusiasm gap” that works against Trump at the midterms. The data suggests, in particular, that the GOP’s initial attempt (and failure) in March to pass its unpopular health care bill may have cost Trump with his core supporters.

At long last, Donald Trump’s base appears to be shrinking. This raises the chances of impeachment, and will put tremendous pressure on Republicans to abandon Trump to preserve their midterm majority. I’m pissed the cause appears to be health care, and not the shady Russian ties or bad behavior, but doing the right thing for the wrong reason is still doing the right thing. It also fits in nicely with current events.

According to the forecast released Wednesday by the nonpartisan Congressional Budget Office, 14 million fewer people would have health insurance next year under the Republican bill, increasing to a total of 19 million in 2020. By 2026, a total of 51 million people would be uninsured, roughly 28 million more than under Obamacare. That is roughly equivalent to the loss in coverage under the first version of the bill, which failed to pass the House of Representatives.

Much of the loss in coverage would be due to the Republican plan to shrink the eligibility for Medicaid; for many others—particularly those with preexisting conditions living in certain states—healthcare on the open marketplace would become unaffordable. Some of the loss would be due to individuals choosing not to get coverage.

The Republican bill, dubbed the American Health Care Act, would also raise insurance premiums by an average of 20 percent in 2018 compared with Obamacare, according to the CBO, and an additional 5 percent in 2019, before premiums start to drop.

So keep an eye on Montana’s special election (I’m writing this before results have come in); if the pattern repeats from previous special elections, Republicans will face a huge loss during the 2018 midterms, robbing Trump of much of his power and allowing the various investigations against him to pick up more steam.