"If you care a lot about the future, it shows that you believe in what you're doing now and you think it's worthwhile enough to have some lasting impact." – Syd Mead
It’s rare to find an amateur documentarian that’s really good. I think this is one of those cases. I was really interested watching “NASA’s Voyager Mission,” by Jackson Tyler (his YouTube channel is “Homemade Documentaries”).
I grew up with Voyager’s mission, from the time when I was 7 years old. I was 9 when Voyagers 1 and 2 reached Jupiter. I was about 19 when Voyager 2 visited Neptune. What I missed was the beginning of the mission. I was too young to keep track of it. I missed the launch of the two probes. So, what’s nice is this documentary covers the beginning, and intimate details of the Grand Tour. It also covers the backstory of when Voyager was planned, in the mid-1960s, who inspired it, and the decisions that were made during the mission’s planning. A surprising thing was the first proposal was just to send these probes to Jupiter and Saturn. A few had the idea to send them to Uranus and Neptune, as well, but they had to fight to get them included in the mission plan.
Something that I found really nice was Tyler went back in history to other scientific observations of Jupiter, Saturn, Uranus, and Neptune, briefly comparing them to what was found through Voyager, and the Cassini probe, giving a sense of the progress in planetary science over the centuries.
Even though I am familiar with what these probes got during the mission, this documentary adds more to what I knew. So, enjoy the feast! Prepare for a long ride, too. It’s 2 hours, 45 minutes.
I happened to find the linked video below, with Prof. Mattias Desmet, a psychoanalytic psychotherapist, discussing this matter with Dr. Reiner Fuellmich, an attorney, and Dr. Wolfgang Wodarg, an internist, pulmonologist, and social medicine specialist, at the Corona Foundation Committee (Stiftung Corona Ausschuss), from August 2021. It struck me as an important discussion, as it gets to the roots of totalitarian political systems that we all need to be aware of.
Edit 8/3/2022: I encourage people to read an addendum I’ve written to this post, dated the same as this edit. I’m leaving this post here, but I’ve changed my mind about it.
Desmet talked about four mass psychological factors that can become present in society, which promote “mass formation,” as he called it, for a totalitarian political system:
Social isolation/lack of social bonds among the mass population
A lack of sense-making in the mass population
Many people experiencing a lot of free-floating anxiety
A lot of free-floating psychological discontent in the population
By “free-floating” he means a sense of “I’m anxious, or I’m feeling angry/depressed/disappointed in life, but I don’t know why.”
He cited as evidence for this (my guess is he was referring to Germany) the amount of antidepressants that were being taken by the population 2-3 years ago, hundreds of millions of doses.
He put emphasis on the fact that free-floating anxiety is the most painful psychological condition a person can experience.
He then discussed the triggers that can move this mass phenomenon toward totalitarianism:
First, mass media in the society provides a “story” (a notion of a sequence of events) that describes an object of anxiety, and at the same time puts forward a convincing strategy for dealing with this anxiety-causing phenomenon. This causes the free-floating anxiety being experienced by the mass population to become defined in the object that is put before them. Now their anxiety is no longer seen as free-floating. It seems to have a cause. People are then willing to implement the strategy they’re given to deal with this object, in an attempt to relieve themselves of the anxiety they’ve been feeling, no matter what the cost.
Second, masses of people engage in what they see as an epic battle with this object of anxiety. This causes a new kind of social bond to emerge between these people who had been socially isolated. Along with that, they collectively find a new kind of sense-making for themselves. It is not rigorous. It is not that rational, but it gives them a sense of making sense of the world they experience. Their life is then directed at battling the object of anxiety. It is through this that they find social connections with other people who are engaged in the same sense of fighting against this object. There is a dramatic flip from social isolation to a massive social connection, through this sense of fighting a war against the cause of their collective anxiety. This then leads to what he described as “mental intoxication,” which is equal to mass hypnosis.
Mass formation is a form of hypnosis
Once this happens, it doesn’t matter whether the story that this population has been given can be rationally, scientifically torn to pieces. What matters is their social connection, which led them to this mental intoxication. They will continue to conduct themselves as if the story is true, no matter what. The reason is they will do anything to avoid going back (this is their fear) to their prior state of free-floating anxiety, where it had no definition, identity, or discernable source, and their previous social isolation. They fear that if they accept anything counter to what brought them out of their prior state, they will go back to their prior state. The motive is as simple as pleasure over pain. Searching for truth is irrelevant.
So, Desmet said, the crucial matter is acknowledging this painful state of anxiety, and then searching for how we got into this state of social isolation, lack of social bond, and lack of sense-making, which led to free-floating anxiety, and massive psychological discontent.
He crystalized this mass social phenomenon as a symptomatic solution to what’s a very real psychological problem.
It’s his contention (and I am sympathetic to this POV) that the sense of crisis over Covid-19 is really much more of a societal and psychological crisis than a biological one.
He said that the mental intoxication that’s experienced leads to a narrowing of attention, to only pay attention to what the story they’ve been given tells them is important. This explains why these people only see the harm done by Covid-19, and are oblivious to the collateral damage done by the lockdowns. They are also unable to feel empathy for the victims of the lockdowns. He emphasized this is not from selfishness, but from the effects of this intoxication, the “mass formation,” as he’s termed it.
He said this effect is so powerful, it so focuses their attention, that you can diminish their physical well-being, and they won’t notice it. This goes back to what he said about how it’s a kind of hypnosis. People who are hypnotized can be injured, and be oblivious to the pain.
A third action that takes place in mass formation is the population at large becomes intolerant of dissonant voices (dissent). I imagine this is because it’s seen as interfering with the sense of social connection, and the intoxication it produces. Again, the people in the throes of this mass phenomenon do this, because they fear going back to their prior state of free-floating anxiety, and social disconnection.
He indicated that mass formation is not widely known among psychologists. They are not aware of it, and so they are not aware of it happening in their world today.
Desmet was asked by Fuellmich what characterizes the totalitarian leaders, “What kind of person does this?”
Desmet said:
They don’t have the same kind of mentality as common criminals, even though their ideology is criminal. They know how to follow their society’s social rules.
When they are in power, they make up their own rules for the society, and follow them.
They are true believers in their ideologies, and they believe they are creating a paradise.
They feel like it’s acceptable to sacrifice a portion of their own population to realize their paradise.
Two books he recommended people read are by Hannah Arendt:
He said that from what’s been observed of such “mass formation” events, it’s impossible to wake up masses of people who are under the influence of it, unless by some catastrophic event. However, he also said free speech is extremely important for tamping down the severity of the crimes committed under these conditions,
You can make the hypnosis less deep by continuing to talk, and that’s what we all have to do.
Dr. Justus Hoffmann, an attorney, made the point that what makes totalitarian regimes so attractive in the short term is that totalitarians create very orderly societies. He said this makes it difficult to talk to people about the danger of such a regime, because they say, “Look, there’s no chaos. … We still have rule of law. Everything’s fine.” Such regimes have a very strict rule of law. He contended they create more law, more agencies, more policing, etc.
Desmet disagreed, saying that there’s a distinction. Totalitarians do not enforce law, they impose rules, and they’re rules that they make up from moment to moment. There is no consistency in either the rules, nor in how they are created.
Desmet talked about a typical distribution with the mass phenomenon: Thirty percent of the population are taken with the story that explains their sense of anxiety, and they create an atmosphere of fear around contradicting that story. Another 40% quietly do not accept the story, but are too afraid to publicly contradict it. There’s another 25-30% who do not accept the story, and speak out.
There was some speculation about what kind of people were resistant to mass formation/the totalitarian drive, and those who are most amenable to it. Desmet seemed more sure about the people who are most likely to join in the mass formation; that they are people who believe they are doing everything to help “the others” (probably society).
Everything is done out of a sense of citizenship. They do it all for the [collective], for the community. They’re convinced of that. That’s also what Hitler said, “I expect of every German that he sacrifices his life without hesitation,” he said, “for the German people.” … That is what Stalin said [as well].
Fuellmich pointed out that it’s been his experience that people who have less formal education, but work a trade, are very educated on weighty issues, and are far more open to having discussions about them than are academics. Desmet responded that Gustav Le Bon saw this in the 19th century, that the higher degree of education you have, the more susceptible you are to mass formation. Viviane Fischer, an attorney, asked why that is. Desmet said that it comes down to what is seen as the purpose of education: Whether it’s an exercise in learning to think for yourself, or whether it’s to convince you to think about everybody else, before yourself. Wodarg added, “You learn to obey.”
They got back to the question of, “What do we do about this?” Desmet threw another activity on the table: Humor is important to “breaking the spell” of mass formation. He said that mass formation relies upon everyone recognizing one authority. The more that someone gives authority to a figure, the more susceptible they are to being hypnotized by that figure. He said it’s important for the humor to be gentle and polite. If it’s too aggressive, it arouses the aggression of the masses. This kind of gentle, polite humor is a good antidote to mass formation, because it subtly delegitimizes the authority without arousing the aggressive response from the masses.
Desmet came back to the topic of cause, though, saying that even if many people come out of their hypnosis in the current sense of crisis, they will fall prey to some other sense of crisis in the future, and go right back into this behavior of mass formation, because what causes this behavior is their sense of anxiousness, disappointment in life, lack of social connection, and lack of sense-making.
He said it’s his educated opinion that a root cause is our culture’s materialistic, mechanistic view of ourselves that causes destruction of our social structures; of social connection, and the feeling in ourselves that “life makes sense.” If you hold the belief that you are just a machine, then by definition, this implies that life is senseless. He asks, what’s the sense of a life that is reduced to just a little part of the larger machine of the Universe? If that’s all we are, then one can reasonably ask what is the point of having meaningful social relations? You don’t have to follow ethical principles, because “the machine” governs what happens and doesn’t happen. There is no right or wrong way for anything to happen. It just is, and will be. This concept destroys one’s “psychological energy,” as he put it, one’s sense of social connectedness, and you end up in this free-floating anxiety he’s talked about.
Wodarg added that in this concept of being “a small piece in the bigger machine,” you also get this sense that you’re a burden for the machine, “It doesn’t need you.” He said the healthier materialist concept is that “You are ‘the machine’. You’re a wonder.” You are not a small cog in the larger mechanism. You are the universe that’s worth something.
Fischer prompted Desmet to take the long view, that the 40% “silent majority” will eventually “run the other way” from this totalitarianism, because a constant in history is that totalitarianism is always self-destructive. The 30% that are hypnotized will never snap out of their delusion, no matter how much destruction happens as the result of their actions and decisions.
Fischer asked whether any sort of positive reward bestowed by the authority on the compliant was necessary to get people to buy in to the totalitarianism. Desmet said that Le Bon observed that the masses prefer harsh and strict leaders who are cruel to their own people. I’m not sure what he meant by “harsh and cruel,” because it hasn’t been my experience that the majority prefers what I think “harsh and cruel” means.
Fischer noted at the end of their discussion that they were livestreaming on a bunch of video services, including YouTube, but that YouTube took down its livestream. That says a lot about them, doesn’t it?…
I’ll end with a nice summary of Solzhenitsyn’s “The Gulag Archipelago,” which covers a couple of the same points:
Edit 10/13/2021: Dr. Peter McCullough, who has been treating Covid patients, has been observing what Dr. Desmet describes, with fellow doctors, and other professionals. He calls it a “trance.” I encourage you to listen to what he says starting at 1:10:00 in the following video, because he illustrated what Desmet was talking about:
The rest of the video is worth watching, as well, but it’s solely on the data relating to Covid treatment, and what therapies have been shown to work.
Edit 1/2/2022: Dr. Robert Malone has come to understand this explicitly. I’m including what he had to say here, as he talks about some promising avenues for breaking the hypnosis. In short, make people aware that there are larger problems than Covid afoot. Sometimes, this happens on its own, as the totalitarianism hits people where they live.
Edit 8/3/2022: It’s not often that I feel like I’ve stepped in it with what I’ve posted on my blog, but I think this is one such case. Take a listen to this podcast with Dr. Peter Breggin, who rips Desmet’s concept of mass formation to shreds. To cut to the chase, advance the slider to 21 mins. The first twenty minutes has Breggin discussing some of his life and background.
At first, I couldn’t understand the disdain that both Catherine Fitts and Breggin expressed for Desmet in this interview, and his notion of mass formation, but I think I came to understand it as I listened to them criticize the book he wrote on this concept, “The Psychology of Totalitarianism.” They were not contradicting the idea that something devastatingly destructive to advanced societies around the world is happening. What they objected to was first, that the ideas about how that’s coming about don’t make any sense, and second, that Desmet’s view of common people is insulting.
I must admit I haven’t read Desmet’s book. All I went on when I posted this was the conference call I linked to at the top of this post, and a few podcasts where he was interviewed. What Fitts and Breggin talked about in the book sounded quite different to me from what I heard him talk about in the call. The only commonality I found between that and his book was how he talked about a mass hypnosis, and how that occurs.
Desmet didn’t put a heavy burden of responsibility on the totalitarian leaders, though. When other parties on the call asked about a “conspiracy” to create a totalitarian society, Desmet sort of waved that away, saying there were some actions that we can see are intentional in that direction, but there are some factors that are effectively “accidental,” that “just happen” in a favorable social environment. According to Fitts and Breggin, Desmet is adamantly against the idea of a conspiracy to create a totalitarian society in his book, saying that any such notions are just a coping mechanism used by intellectuals to assuage their “needs” in the face of the alarming things they’re seeing. In the view of Fitts and Breggin, the moves toward a totalitarian society we are seeing are being strongly forced. There is nothing “natural” about this.
Where the book really differs from what I heard in the call was it seems to say that totalitarian leaders bear no responsibility for the society they create, that they’re just responding to the demand for totalitarian leadership from the masses, which have fallen into their deranged state through circumstances beyond their control. Fitts and Breggin also said the book takes a very dim view of “the masses,” saying they’re effectively “useless.” If this is indeed what the book says (Fitts and Breggin make in my mind a compelling case that it does), they are views that I cannot endorse on an ethical level, and they surprise me. I didn’t pick up any hints of this in Desmet’s call with the other participants.
The only part of the discussion with Breggin where I felt like I differed with him was where he said that Desmet had a self-contradicting notion in mass formation, talking about how the hypnotized masses “all move together in formation.” He said it would be very difficult for them to do so, “since they’re all isolated.” In the call, Desmet talked about a process through time, and at least what I took from it was that first, masses of people are isolated, but eventually they come out of that isolation. After they’ve been “hypnotized” through consistent messaging through mass media, the “hypnotized” find each other, and experience the exaltation of finding people with the same previous mental malady of “free-floating anxiety,” and which now have a common enemy, which they think has caused their anxiety. So, Breggin’s notion that “they just stay isolated” doesn’t make sense to me, but perhaps this is how it’s expressed in the book.
Breggin gave Desmet a little credit, saying there were behaviors he identified in his notion of mass formation that are real, but he said where Desmet goes wrong is he attributes them to things that have no basis. For example, he said that where Desmet and others see “hypnosis” is actually the result of a deliberate process of mental entrainment, which cognitively is a different process.
At about an hour into the interview, Fitts and Breggin talked about what they thought from their experience was a more realistic explanation for what we’ve seen, which is that there really are psychopaths in the world that organize themselves politically, grab power, and want to control large masses of people. In the process, they cause great harm. We’ve seen that in history, and that’s what we’re experiencing right now, not just in one or a few countries, but many countries around the world.
They made reference to a couple books as backgrounders for their discussion about Desmet and his book. One is by Peter Breggin and his wife, Ginger, “Covid-19 and the Global Predators: We Are The Prey,” and, “Political Ponerology,” by Andrew M. Lobaczewski. Both are by authors who have sought to understand what creates totalitarian societies, and what constitutes it. My interest in posting this article in the first place was about helping people understand this. So, I hope what I’ve said generates further interest in this subject, because it is a critical one to understand.
Something I’ll make a note about here re. the discussion between Fitts and Breggin is that I think a lot of people will likely feel uncomfortable with a particular feature of their discussion, which is their use of the word “they” a lot, without identifying who they’re talking about. This is a very amorphous concept that most of us are not accustomed to, and many are suspicious of, particularly among the more rational, because, “What’s the difference between something you can’t define and it not existing at all?” To really understand this background might require reading the book on Covid-19 I mentioned in the above paragraph. I don’t know. I haven’t read it yet (though it’s on my reading list). I’ve listened to an interview with Fitts previously, and I get the impression she knows of what she speaks when she talks about people in high-powered positions in our society, and in government, who have done some nefarious things in the past that have had historical consequences. She’s said that she met such people while in government service. She has a sense of knowing how they think, and what they’re capable of. What feels kind of grating is she doesn’t name anybody when she talks about this stuff. So, it’s difficult to tell if she’s talking about real people or events, or if her past experience has spooked her enough that she’s speculating in an unwarranted way. From where I sit, it’s hard to tell. I don’t know her. All I can rely on is my judge of character. She doesn’t strike me as being that paranoid. Though, from what she describes in the interview, she seems to have to check her back from time to time. Anyway, I found this discussion worth listening to as a valid criticism of Desmet’s notion of mass formation.
Philosopher Matthew Crawford talked in the interview below about the nature of what science in its technical practice has become, at least in certain fields, which takes it away from its telos. He blames what I’ve heard termed “big science,” because it’s made scientific research big and bureaucratic, requiring the raising of lots of money to build equipment, and to maintain it, so that scientists can push the boundaries of what we know. The problem is the nature of the organization that’s necessary to build this apparatus is political. And so politics is going to be a part of what’s happening with it, while scientists are trying to work within these organizations to carry out their research. It inevitably comes into their research, as part of these organizations, because the power dynamic within them favors the political actors over the search for truth.
What this suggests to me is that “big science” has a point of diminishing returns, where once you reach a tipping point, the endeavor becomes more political than scientific, and so there really isn’t a point in going further in the growth of these particular, ostensibly scientific institutions, because the political focus of the organization just increases as it grows, crowding out the science that it was originally intended to foster. He also discussed some dynamics that have occurred with the climate issue, specifically, as illustrations of this social effect he was talking about.
I liked reading Giving Up Darwin: A fond farewell to a brilliant and beautiful theory, by David Gelernter, because it’s the most thought-provoking article I’ve read in a long time. As I read it, I really wondered if he was going to come out as a believer in Intelligent Design, because he says that theory makes some important points about Darwinian evolution, but that’s not where he goes. He doesn’t reveal this until the end, where he pokes holes in ID, as well. Really what he says is we need a new theory. Some aspects of Darwin’s theory of evolution still hold, but some need reconsideration, because accumulating evidence falsifies them.
I’d think to a scientist, this is an exciting prospect, because it means there’s something significant to discover about the morphogenesis of the species we see in the fossil record.
Edit 2/17/2022: The video below by Anton Petrov illustrates what Gelernter was talking about, that evolution is not completely random. This is being called genetic bias. What some molecular biologists who studied this found is that genetic bias is due to certain essential genes being protected more robustly by DNA repair mechanisms than others. They are also possibly protected by proteins.
Petrov makes an interesting point that since “living fossils” have been found, organisms that were once thought extinct, this means that evolution for some organisms stopped millions of years ago. They have so much protection against mutation that they change very little, or not at all over eons.
In another example, he talked about how a genetic bias has been found for mutation in the HbS protein in people in a large part of the African continent, and some parts of southern Europe, that either protects people against malaria, or produces sickle cell anemia. The European region for this is interesting, because the people there are not in danger of getting malaria. Yet, some of them still have this mutation.
This bias is only evident in populations that call these regions home, for some reason. It’s not evenly distributed in populations across the world. This seems to suggest an environmental pressure on this bias, but that hasn’t been determined yet.
It has become apparent to me that just as Darwin’s theory of natural selection was once controversial in society, particularly as it applied to human origins, modern science continues to upset people. We also have this confusing thing going on where our society claims to own scientific knowledge, when science disagrees with what it’s doing, and so society fails to reach its stated goals, and we blame non-factors for the failure. We are acting quite superstitious. What doesn’t help is that we have people with the title of scientist who are espousing knowledge not based in science, but which is accepted as “official science” that everyone is expected to believe and follow. It’s not unusual, though. Thomas Sowell wrote about it in his book, “Intellectuals and Society,” saying that some politicians reverse the process of discovery. Rather than following the evidence, they hire experts who will massage the evidence to fit the politicians’ desired agenda, and basically rubber stamp it (without appearing publicly to do so). That doesn’t always happen, but it happens enough that it negatively affects our society. I’d like to share Dr. Morrissey’s contrasting account about his knowledge and experience on disease, and what is actually being enforced in government policy in various places around the world (follow link below). It’s a tragic story, and I think it deserves to be highlighted, because it’s really a choice between knowledge and ignorance, and the joy and suffering that each brings.
The second topic that is not being addressed in our public discussions, because it seems verboten, is risk. What I see frequently is that too many in advanced societies are not mature enough to discuss it. It seems many are not experienced in taking risks, and what that means. They may only be experienced in the notion of tragedy, and any notion of taking a risk is disgusting to them. Though, in fact, they take risks all the time. I’ve seen an increasing trend since the 1990s of people who say that all risk must be eliminated. They are saying the equivalent that they demand the defeat of gravity. It can’t be done. What are we willing to sacrifice on the altar of this impossibility?
A while back, Alan Kay and I got into a discussion about what a computer is, and he wished to correct my notion of them. I had this idea that a computer is something that can do an operation (like store/fetch memory, do an arithmetic operation), do comparisons, branch, and do this repeatedly, without the need of human intervention. I contrasted this with a typical, non-programmable calculator, which I thought wasn’t a computer. He said that a computer is something that can help people realize larger ideas, that it doesn’t necessarily need what I outlined, and that even a calculator is a computer. He said you can make a simple computer using two rulers. He used this example with children when he was involved with education.
I came upon “Hands-On: Smarty Cat is Junior’s First Slide Rule” from Hackaday. The main subject is on a children’s version of the slide rule, called Smarty Cat, that can do addition and subtraction, and multiplication and division–a four-function calculator for integers. The article also shows the two-ruler example that Alan talked about, to do addition and subtraction on integers and some rational numbers. It uses this as an intro. to talking about real slide rules. They operate on the same principle, but facilitate more sophisticated operations.
This is one of a series of “bread crumb” articles I’ve written. To see more like this, go to the Bread Crumbs page.
I’d heard about Mensa many years ago, and for many years I was kind of interested in it. Every once in a while I’d see “intelligence quizzes,” which were supposed to get one interested in the group (it worked). Mensa requires an IQ test, and a minimum score, to join. Nevertheless, I looked at some samples of the discussions members had on topics related to societal issues, though, and it all looked pretty mundane. It wasn’t the intelligent discussion I expected, which was surprising. Later, I found out I’m below their entrance threshold. Based on taking a peek, though, I don’t feel like I’m missing anything.
I came upon a video by Stefan Molyneux recently, “Mensa Statists and the Aneurysm of Truth” (it was made in 2012), and it seems to explain what I’ve been seeing generally for more than ten years in the same sort of societal discussions (though I can’t say what the IQ level of the participants was). I’ve frequently run into people who seem to have some proactive mental ability, and yet what they come out with when thinking about the society they live in is way below par. I see it on Quora all the time. Most of the answers to political questions are the dregs of the site–really bad. I’ve had no explanation for this inconsistency, other than perhaps certain people with less than stellar intelligence are drawn to the political questions, until I saw this analysis. Molyneux said it’s the result of a kind of cognitive abuse.
The reason I’m bothering with this at all is seeing what he described play out has bothered me for many years, though I’ve assumed it’s due to popular ignorance. It’s part of what’s driven my desire to get into education, though now I feel I have to be more humble about whether that’s really a good answer to this.
I found his rational explanation for this confusing. I needed to listen to it a few times, and take notes. I’ll attempt to summarize.
This is a generalization, but the point is to apply it to people who are more intelligent than average, and who refuse to allow inquiry into their beliefs about society:
Children who are in the “gifted” categories of IQ are told a certain moral message when they’re young, about how they are to behave. However, when those same children try to apply that morality to their parents, and the adults around them–in other words, demand consistency–they are punished, humiliated, and/or shamed for it. They eventually figure out that morality has been used to control them, not teach them. (This gave me the thought, based on other material by Molyneux, that perhaps this is one reason atheism is so prevalent among this IQ category. Rather than morality being a tool to uplift people to a higher state of being, it’s seen purely as a cynical means of control, which they understandably reject.) As soon as they try to treat morality as morality, in other words, as a universal set of rules by which everyone in their society is governed, they are attacked as immoral, uncaring, brutish, wrong, and are slandered. This is traumatic to a young mind trying to make sense of their world.
The contradiction they encounter is they’re told they’re evil for not following these rules as a child, and then they’re told they’re evil for attempting to apply those same rules to other adults when they grow up. They are punished for attempting to tell the truth, even though they were told when they were young that telling the truth is a virtue (and that lying is evil). If they attempt to tell the truth about their society, they are punished by the same adults who cared for them.
The image he paints is, to me, analogous to Pavlov’s dog, where all of its attempts to follow its instincts in a productive way are punished, leading to it quivering in a corner, confused, afraid, and despondent, unable to respond at all in the presence of food. In this case, all attempts to apply a moral code consistently are punished, leading to a disabled sense of social morality, and a rejection of inquiry into this battered belief system, in an attempt to protect the wound.
Molyneux comes to an ugly truth of this situation. This inability to question one’s societal beliefs is the product of a master-slave society: In slave societies, rules are applied to the slaves that are not applied to the masters. They operate by a different set of rules. Morality that is dispensed to the ignorant is used as a cynical cover for control. Those subjected to this inconsistent reality deal with it by trying their best to not look at it. Instead of pushing through the shaming, and demanding consistency, risking the rejection that entails from the society in which they grew up, they blindly accept the master-slave dichotomy, and say, “That’s just the way it is.” Those who question it are attacked by these same people, because engaging in that leads them back to the pain they suffered when they did that themselves.
He also addressed a psychological phenomenon called “projection.” He said,
… they must take the horrors of their own soul and project them upon the naive and honest questioner. Every term that is used as an attack against you for engaging in these conversations is an apt and deeply known description of their own souls, or what’s left of them.
Molyneux sort of addressed the evolutionary reasons for motivated reasoning in another video, “The Death of Reason: Why People Don’t Listen to Reason and Evidence”, but I have liked Jonathan Haidt’s explanation for it better, since he gets into the group dynamic of shared beliefs, and justifies them, saying that they played some role in the survival of our species, up until recently: Those who had this group-belief trait lived to reproduce. Those who did not died out. That isn’t to say that it’s essential to our survival today, but that it deserves our respectful treatment, since it was a trait that got what we are here.
What’s also interesting is that Molyneux related the trait of motivated reasoning to the practice of science, quoting Max Planck (I’ve heard scientists talk about this) in saying that science really only advances when the older generation of scientists dies. This creates room for other ideas, supported by evidence, and critical analysis, to flourish, perhaps setting a new paradigm. If so, it becomes a new sort of orthodoxy in a scientific discipline for another generation or so, until it (the orthodoxy), too, dies away with the scientists who came up with it, repeating the cycle.
If you’ve been reading along with my posts on exercises from “Structure and Interpretation of Computer Programs” (SICP), this is going to come pretty late. The book is a math-heavy text. It expects you to know the math it presents already, so for someone like me who got a typical non-math approach to math in school, it seems abrupt, but not stifling. If you’re wondering what I mean by “non-math approach,” I talked about it in “The beauty of mathematics denied,” James Lockhart also talked about it in “A Mathematician’s Lament.”
I’ve been reading a book called, “Mathematics in 10 Lessons: The Grand Tour,” by Jerry King (I referred to another book by King in “The beauty of mathematics denied”), and it’s helped me better understand the math presented in SICP. I could recommend this book, but I’m sure it’s not the only one that would suffice. As I’ve gone through King’s book, I’ve had some complaints about it. He tried to write it for people with little to no math background, but I think he only did an “okay” job with that. I think it’s possible there’s another book out there that does a better job at accomplishing the same goal.
What I recommend is getting a book that helps you understand math from a mathematician’s perspective before getting into SICP, since the typical math education a lot of students get doesn’t quite get you up to its level. It’s not essential, as I’ve been able to get some ways through SICP without this background, but I think having it would have helped make going through this book a little easier.
This is one of a series of “bread crumb” articles I’ve written. To see more like this, go to the Bread Crumbs page.
A couple questions have bugged me for ages about rational numbers:
Why is it that we invert and multiply when dividing two fractions?
Why is it that when we solve a proportion, we multiply two elements, and then divide by a third?
For example, with a proportion like:
the method I was taught was to cross-multiply the two numbers that are diagonally across from each other (2 and 180), and divide by the number opposite x (3). We solve for x with , but why?
These things weren’t explained. We were just told, “When you have this situation, do X.” It works. It produces what we’re after (which school “math” classes see as the point), but once I got into college, I talked with a fellow student who had a math minor, and he told me while he was taking Numerical Analysis that they explained this sort of stuff with proofs. I thought, “Gosh, you can prove this stuff?” Yeah, you can.
I’ve picked up a book that I’d started reading several years ago, “Mathematics in 10 Lessons,” by Jerry King, and he answers Question 1 directly, and Question 2 indirectly. I figured I would give proofs for both here, since I haven’t found mathematical explanations for this stuff in web searches.
I normally don’t like explaining stuff like this, because I feel like I’m spoiling the experience of discovery, but I found as I tried to answer these questions myself that I needed a lot of help (from King). My math-fu is pretty weak, and I imagine it is for many others who had a similar educational experience.
I’m going to answer Question 2 first.
The first thing he lays out in the section on rational numbers is the following definition:
I guess I should explain the double-arrow symbol I’m using (and the right-arrow symbol I’ll use below). It means “implies,” but in this case, with the double-arrow, both expressions imply each other. It’s saying “if X is true, then Y is also true. And if Y is true, then X is also true.” (The right-arrow I use below just means “If X is true, then Y is also true.”)
In this case, if you have two equal fractions, then the product equality in the second expression holds. And if the product equality holds, then the equality for the terms in fraction form holds as well.
When I first saw this, I thought, “Wait a minute. Doesn’t this need a proof?”
Well, it turns out, it’s easy enough to prove it.
The first thing we need to understand is that you can do anything to one side of an equation so long as you do the same thing to the other side.
We can take the equal fractions and multiply them by the product of their denominators:
by cancelling like terms, we get:
This explains Question 2, because if we take the proportion I started out with, and translate it into this equality between products, we get:
To solve for x, we get:
which is what we’re taught, but now you know the why of it. It turns out that you don’t actually work with the quantities in the proportion as fractions. The fractional form is just used to relate the quantities to each other, metaphorically. The way you solve for x uses the form of the product equality relationship.
To answer Question 1, we have to establish a couple other things.
The first is the concept of the multiplicative inverse.
For every x (with x ≠ 0), there’s a unique v such that xv = 1, which means that .
From that, we can say:
From this, we can say that the inverse of x is unique to x.
King goes forward with another proof, which will lead us to answering Question 1:
Theorem 1:
Proof:
by cancelling like terms, we get:
(It’s also true that , but I won’t get into that here.)
Now onto Theorem 2:
By Theorem 1, we can say:
We can use the multiplicative inverse of , applying it to both sides, to get,
By cancelling like terms, we get:
Therefor,
And there you have it. This is why we invert and multiply when dividing fractions.
Edit 1/11/2018: King says a bit later in the book that by what I’ve outlined with the above definition, talking about how if there’s an equality between fractions, there’s also an equality between a product of their terms, and by Theorem 1, it is mathematically correct to say that division is just a restatement of multiplication. Interesting! This does not mean that you get equal results between division and multiplication: , except when b equals 1 or -1. It means that there’s a relationship between products and rational numbers.
Some may ask, since the mathematical logic for these truths is fairly simple, from an algebraic perspective, why don’t math classes teach this? Well, it’s because they’re not really teaching math…
Note for commenters:
WordPress supports LaTeX. That’s how I’ve been able to publish these mathematical expressions. I’ve tested it out, and LaTeX formatting works in the comments as well. You can read up on how to format LaTeX expressions at LaTeX — Support — WordPress. You can read up on what LaTeX formatting commands to use at Mathematical expressions — ShareLaTeX under “Further Reading”.
HTML codes also work in the comments. If you want to use HTML for math expressions, just a note, you will need to use specific codes for ‘<‘ and ‘>’. I’ve seen cases in the past where people have tried using them “naked” in comments, and WordPress interprets them as HTML tags, not how they were intended. You can read up on math HTML character codes here and here. You can read up on formatting fractions in HTML here.
SICP reaches a point, in Chapter 3, where for significant parts of it you’re not doing any coding. It has exercises, but they’re all about thinking about the concepts, not doing anything with a computer. It has you do substitutions to see what expressions result. It has you make diagrams that focus in on particular systemic aspects of processes. It also gets into operational models, talking about simulating logic gates, how concurrent processing can work (expressed in hypothetical Scheme code). It’s all conceptual. Some of it was good, I thought. The practice of doing substitutions manually helps you really get what your Scheme functions are doing, rather than guessing. The rest didn’t feel that engaging. One could be forgiven for thinking that the book is getting dry at this point.
It gets into some coding again in Section 3.3, where it covers building data structures. It gets more interesting with an architecture called “streams” in Section 3.5.
One thing I will note is that the only way I was able to get the code in Section 3.5 to work in Racket was to go into “Lazy Scheme.” I don’t remember what language setting I used for the prior chapters, maybe R5RS, or “Pretty Big.” Lazy Scheme does lazy evaluation on Scheme code. One can be tempted to think that this makes using the supporting structures for streams covered in this section pointless, because the underlying language is doing the delayed evaluation that this section implements in code. Anyway, Lazy Scheme doesn’t interfere with anything in this section. It all works. It just makes the underlying structure for streams redundant. For the sake of familiarity with the code this section discusses (which I think helps in preserving one’s sanity), I think it’s best to play along and use its code.
Another thing I’ll note is this section makes extensive use of knowledge derived from calculus. Some other parts of this book do that, too, but it’s emphasized here. It helps to have that background.
I reached a stopping point in SICP, here, 5 years ago, because of a few things. One was I became inspired to pursue a history project on the research and development that led to the computer technology we use today. Another is I’d had a conversation with Alan Kay that inspired me to look more deeply at the STEPS project at Viewpoints Research, and try to make something of my own out of that. The third was Exercise 3.61 in SICP. It was a problem that really stumped me. So I gave up, and looked up an answer for it on the internet, in a vain attempt to help me understand it. The answer didn’t help me. It worked when I tried the code, but I found it too confusing to understand why it produced correct results. The experience was really disappointing, and disheartening. Looking it up was a mistake. I wished that I could forget I’d seen the answer, so I could go back to working on trying to figure it out, but I couldn’t. I’d seen it. I worked on a few more exercises after that, but then I dropped SICP. I continued working on my history research, and I got into exploring some fundamental computing concepts on processors, language parsing, and the value of understanding a processor as a computing/programming model.
I tried an idea that Kay told me about years earlier, of taking something big, studying it, and trying to improve on it. That took me in some interesting directions, but I hit a wall in my skill, which I’m now trying to get around. I figured I’d continue where I left off in SICP. One way this diversion helped me is I basically forgot the answers for the stuff I did. So, I was able to come back to the problem, using a clean slate, almost fresh. I had some faded memories of it, which didn’t help. I just had to say to myself “forget it,” and focus on the math, and the streams architecture. That’s what finally helped me solve 3.60, which then made 3.61 straightforward. That was amazing.
A note about Exercise 3.59
It was a bit difficult to know at first why the streams (cosine-series and sine-series) were coming out the way they were for this exercise. The cosine-series is what’s called an even series, because its powers are even (0, 2, 4, etc.). The sine-series is what’s called an odd series, because its powers are odd (1, 3, 5, etc.). However, when you’re processing the streams, they just compute a general model of series, with all of the terms, regardless of whether the series you’re processing has values in each of the terms or not. So, cosine-series comes out (starting at position 0) as: [1, 0, -1/2, 0, 1/24, …], since the stream is computing a0x0 + a1x1 + a2x2 …, where ai is each term’s coefficient, and some of the terms are negative, in this case. The coefficients of the terms that don’t apply to the series come out as 0. With sine-series, it comes out (starting at position 0) as: [0, 1, 0, -1/6, 0, 1/120, …].
What’s really interesting is that exercises 3.59, 3.61, and 3.62 are pretty straightforward. Like with some of the prior exercises, all you have to do is translate the math into stream terms (and it’s a pretty direct translation from one to the other), and it works! You’re programming in mathland! I discovered this in the earlier exercises in this section, and it amazed me how expressive this is. I could pretty much write code as if I was writing out the math. I could think in terms of the math, not so much the logistics of implementing computational logic to make the math work. At the same time, this felt disconcerting to me, because when things went wrong, I wanted to know why, computationally, and I found that working with streams, it was difficult to conceptualize what was going on. I felt as though I was just supposed to trust that the math I expressed worked, just as it should. I realize now that’s what I should have done. It was starting to feel like I was playing with magic. I didn’t like that. It was difficult for me to trust that the math was actually working, and if it wasn’t, that it was because I was either not understanding the math, and/or not understanding the streams architecture, not because there was something malfunctioning underneath it all. I really wrestled with that, and I think it was for the good, because now that I can see how elegant it all is, it looks so beautiful!
Exercise 3.60
This exercise gave me a lot of headaches. When I first worked on it 5 years ago, I kind of got correct results with what I wrote, but not quite. I ended up looking up someone else’s solution to it, which worked. It was kind of close to what I had. I finally figured out what I did wrong when I worked on it again recently: I needed to research how to multiply power series, but in a computationally efficient manner. It turns out you need to use a method called the Cauchy product, but there’s a twist, because of the way the streams architecture works. A lot of math sources I looked up use the Cauchy product method, anyway (including a source that covers power series multiplication that I cite below), but the reason it needs to be used is it automatically collects all like terms as each term of the product is produced. The problem you need to work around is that you can’t go backwards through a stream, except by using stream-ref and indexes, and I’ve gotten the sense by going through these exercises that when it comes to doing math problems, you’re generally not supposed to be doing that, though there’s an example later in SICP where they talk about a method Euler devised for accelerating computation of power series where they use stream-ref to go backwards and forwards inside a stream. I think that’s an exception.
Here are a couple sources that I found helpful when trying to work this out:
Formal Power Series, from Wikipedia. Pay particular attention to the section on “Operations on Formal Power Series.” It gives succinct descriptions on multiplying power series, inverting them (though I’d only pay attention to the mathematical expression of this in Exercise 3.61), and dividing them (which you’ll need for Exercise 3.62).
Edit 6/4/2018: I originally had a video here, which I thought gave a good illustration of what the Cauchy product accomplishes. It also provided a nice visual aide that pointed me toward a solution to this problem in SICP. Unfortunately, the video has disappeared from YouTube. So, I’ll substitute a presentation of the Cauchy product that I used as a tool for figuring out how to do this exercise. This will not give you the answer for how to do this exercise, but it’s on the way to the answer I got.
Let A and B be power series that we’re going to multiply. We will use ai to represent the coefficients for A, and bi to represent the coefficients for B:
A = a0x0 + a1x1 + a2x2 + …
B = b0x0 + b1x1 + b2x2 + …
Multiplying these series creates a new series, C, made by creating a sum of products from terms in A and B:
A x B = C
C0 = a0x0b0x0
C1 = a1x1b0x0 + a0x0b1x1
C2 = a2x2b0x0 + a1x1b1x1 + a0x0b2x2
C3 = a3x3b0x0 + a2x2b1x1 + a1x1b2x2 + a0x0b3x3
C4 = …
A x B = C0 + C1 + C2 + C3 + C4 + …
You’ll note that, with the exception of the very first term, as we progress to computing each term, we start with the ith term in series A, and go down to the 0th term, but with series B, we start with the 0th term, and go upward to the ith term.
To reiterate, you can’t use the stream architecture in SICP to compute the product for this exercise using the exact method I’ve outlined above (when I thought about trying to do that, it get extremely convoluted, and it’s not worth pursuing), but there is a way to compute the product series that allows you to go through both streams from left to right.
What helped me find a succinct way to implement mul-series was to just focus on the coefficients:
There is a way to do the Cauchy product without using mutable state in variables, nor is it necessary to do anything particularly elaborate. You can do it just using the stream architecture.
Think about how addition is commutative, as you look at the above pattern of computation.
The solution is a little counterintuitive, but once you find it, it’s pretty neat.
It is crucial that you get the solution for this exercise right, though, because the next two exercises (3.61 and 3.62) will give you no end of headaches if you don’t. Exercise 3.61 builds on what you create for this one, and 3.62 builds on what you create for 3.61.
Exercise 3.60 says you can try out mul-series using sin(x) and cos(x), squaring both, and then adding the product series together. This should give you a result of 1. How is “1” represented in streams, though? Well, it makes sense that it will be in the constant-term position (the zeroth position) in the stream. That’s where a scalar value would be in a power series.
There is a related concept to working with power series called a unit series. A unit series is just a list of the coefficients in a power series. If you’ve done the previous exercises where SICP says you’re working with power series, this is what you’re really working with (though SICP doesn’t mention this). It’s why in Exercise 3.61 SICP has you writing a function called “invert-unit-series”.
The unit series equivalent for the scalar value 1 is [1, 0, 0, 0, 0, …].
A note about Exercise 3.62
The exercise talks about using your div-series function to compute tan-series. Here was a good source for finding out how to do that:
, but why?
.
, but I won’t get into that here.)
, applying it to both sides, to get,
, except when b equals 1 or -1. It means that there’s a relationship between products and rational numbers.
Tekkie 