A Drifter:

one that drifts
especially: one that travels or moves about aimlessly

Chapter One In Search of Inifinity:

On a personal note, immersing myself in this book—its exploration of infinity and a somewhat outdated cosmology—creates a welcome distance from the constant stream of everyday impressions, such as the political madness of the Russia–Ukraine conflict. Thinking back to what I wrote yesterday, I’m reminded that the deepest, and perhaps truly important, events are not the loudest ones. Books that are so absorbing that the loudest or most obvious happenings around us temporarily lose their volume or their apparent significance have a special value.

I also find that many Russian scholars from the Soviet era wrote exceptionally clear books—even in English translation. One that immediately comes to mind is A. Khinchin’s remarkably lucid introduction to mathematical analysis.

This book consists of four chapters. I will collect notes for each chapter here, and once I have finished all four, I will post a full review.

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“The idea of the infinite in science came from various sources. The questions: Is the universe bounded? Did it have a beginning? Will it have an an end? were one such source.”

“One of the most vital questions that ancient Greek philosophers contended with was the structure of the world in the small . Daily experience showed that a loaf of bread could be shared by two, three, or at most ten people, and it could be broken into some ten thousand crumbs. Could the loaf of bread be further subdivided? And is there a limit to divisibility of material objects? Experience alone could not supply an answer to this question, and so the question of the limits of divisibility of objects shifted from the realm of experience to that of speculation.”

"The fifth reason - the reason Aristotle regarded as the weightiest - was that there are no bounds to thought. Specifically, there are no bounds on numbers, or on mathematical magnitudes, or on what is beyond heaven. And if what is beyond heaven is infinite, then there are many worlds."

"The first arises as a result of successive and unlimited addition of new objects, and the second is the result of delving indefinitely deeper into the structure of an object under investigation."

"Unlike Plato, who thought that the world was the work of a Demiurge (creator), Aristotle claimed that it was not created and was eternal."

"To avoid the use of the infinite, Euclid's predecessor, the Greek mathemati­cian Eudoxus formulated an axiom which, in effect, denied the existence of infinitely small and infinitely large magnitudes."

"Cusa developed the doctrine of the maximum, that is something that cannot be ex­ ceeded."

"But times were changing. To solve practical problems scientists found it necessary to apply methods forbidden by Aristotelian science and to use indivisible and infinitely small magnitudes."

"Toward the end of the 17th century Newton and Leibniz independently systematized the methods of solution of a tremendous variety of problems, methods based on the use of infinitely small and infinitely large magnitudes."

“In astronomy, physics and mathematics, the end of the 17th century witnessed the triumph of ideas connected, in one way or another, with the use of the infinite”

“Einstein wrote: Newton found that observed geometric magnitudes (distances be­tween material points) and their changes in time do not, in a physi­cal sense, fully characterize motion . . . Thus, in addition to masses and to distances between points that change in time there exists something else that determines the occurring events; this "some­thing" he took to be the relation to absolute space.”

“The students and followers of Newton and Leibniz used the vague concepts of the infinitely small and infinitely large, full of mystery, to sol ve the most complex problems of astronomy, physics and mechanics. They proceeded recklessly. They unceremoniously added infinitely many terms without pausing to ask whether or not the rules of operation applicable to finite sums carried over to infinite sums.”

“But at the end of the 18th century came the first signs of trouble. Cases began to accumulate where incorrect application of infinitely small and infinitely large magnitudes led to paradoxes. As a result, in the beginning of the 19th century these magnitudes were banished from mathematics and replaced by the idea of limit. In this the works of Abel , Cauchy, and Gauss,  the "prince ofmathematicians," played a collective role. The following excerpt from Gauss' letter to Schumacher, written in 1 83 1 , is typical of his view of the infinite:

"I object to the use of an infinite magnitude as something completed; this is never admissible in mathematics. One must not interpret infinity literally when, strictly speaking, one has in mind a limit ap­proached with arbitrary closeness by ratios as other things increase without bounds."

Another area where complications arose was cosmology. The natural as­sumptions about the uniform distribution of stars in infinite space led unexpectedly to a paradox. It turned out that their collective brightness would be thesame as if a Sun glittered at every point in the sky.

It was an image an Indian poet had in mind many centuries earlier when he exclaimed:

The sky above would shine
With boundless and awesome force
If a thousand Suns at once flashed in it."

“Riemann dealt with the problem of curvature of space in his inaugural lecture of 1854. At that time, the (laudable) custom was that a beginning instructor was expected to present a lecture before the members of the faculty who would then be in a position to judge his teaching abilities. Riemann offered a few topics for such a lecture and Gauss selected the one that interested him most - "On the hypotheses which lie at the foundations of geometry." It is safe to assume that the listeners were not greatly impressed by Riemann's pedagogical talent. The only listener who completely understood Riemann's lecture was Gauss.”

“Whereas, as noted earlier, in Newton 's physics space was completely independent of the matter in it, the new theory ruled out the very existence of empty, that is field-free, space. Also, it turned out that space and time cannot exist independently, but only in a state of inseparable connection with one another, and only as a structural property of a field.”

"After the appearance of dynamic models of the Universe there arose a number of questions now pondered by theoretical physicists : When did the scattering of the galaxies begin and what preceded it?Will the scattering persist forever or will there be a period of contraction? and so on. Today most scientists agree that many billions of years ago the Universe was in a superdense state. It appears that the density of this clot was greater than the density of matter in atomic nuclei - that is, greater than ... g/cm³.

Some computations give densities of the order of ... g/cm^3 . One thing is clear, namely that matter was in a state completely unknown to today 's physicists, and that neither gravitational laws nor quantum theory were applicable to it. Of all these theories (including the "big bang") the eminent physicist L.N. Brillouin  said that "all this is too beautiful to be true and too unlikely to be believed." Nevertheless, modern science has no other theory that explains the multitude of puzzling phenomena in the Universe."

“Another question of interest to scientists is, of course, the future of theUniverse. Here there are two possible scenarios: either the Universe will continue to expand indefinitely and at some very distant time the galaxies will have drifted so far apart that the inhabitants of one won'tt be able to see any of the others, or at some moment the scattering of the galaxies will be arrested and they will begin to come closer to one another. Computations show that which of these tendencies will prevail depends on the average density of matter in the Universe. Computations show that which of these tendencies will prevail depends on the average density of matter in the Universe. If this density is less than ... , then expansion will continue forever. Otherwise, at some moment, the Universe will begin to contract. Some scientists believe that the contraction will continue until the Universe will again achieve the state of a superdense clot and the same chain of events will again unfold. One cannot help but remember the words of Heraclitus about the fire that regularly blazes up and is regularly extinguished."

"And what, in fact, is the density of matter in the Universe? What makes it difficult to answer this question is the possibility that a great part of matter is in a state that makes observations impossible."

"At the moment there are no conceivable methods of disproving the claim that our Universe is closed and
that its size does not exceed 10^25 km."

-----

grok:

"Chapter One of In Search for Infinity traces humanity’s long, uneasy confrontation with the idea of the infinite—from ancient philosophy through 20th-century cosmology and physics. It shows how the infinite repeatedly appeared as both an indispensable tool and a source of paradoxes, forcing science to alternately embrace, banish, and finally rigorize it.

Key historical stages

1. Ancient Greece and the birth of the problem
   • Questions about the cosmos (“Is the universe bounded? Did it have a beginning?”) and about matter (“Is divisibility unlimited?”) pushed thought beyond experience into speculation.
   • Aristotle rejected actual infinity but accepted potential infinity. He argued that the world is eternal (not created), and that thought itself has no bounds—numbers, magnitudes, and what lies “beyond heaven” can grow without limit. 
2. Classical mathematics avoids the infinite
   • Euclid and Eudoxus deliberately constructed geometry without infinitely large or infinitely small quantities.
   • Medieval thinkers like Nicholas of Cusa introduced the idea of a maximum that cannot be exceeded, but still kept infinity theological rather than scientific.
3. 17th century: The reckless triumph of the infinite
   • Practical needs (ballistics, astronomy, mechanics) forced scientists to use infinitely small and infinitely large magnitudes despite philosophical prohibitions.
   • Newton and Leibniz independently created the calculus, systematizing these “vague and mysterious” concepts. Their followers applied infinitesimal methods with enormous success and little rigor—adding infinite series, discarding infinite terms, etc., “recklessly” but fruitfully.
4. Late 18th–early 19th century: Crisis and purification
   • Paradoxes began to pile up (e.g., divergent series giving nonsense results).
   • Mathematicians (Abel, Cauchy, Gauss) banished actual infinitesimals, replacing them with the rigorous concept of limit.
5. Cosmology and physics: New infinities, new paradoxes
   • Assuming an infinite, uniform distribution of stars led to the famous “photometric paradox” (the night sky should be infinitely bright—an image anticipated centuries earlier by an Indian poet’s vision of a thousand suns).
   • Newton’s absolute space and time were challenged by relativity: Einstein showed that space-time is not an independent container but a structural property of gravitational fields; empty space cannot exist.
6. 19th–20th century geometry and cosmology
   • Riemann’s 1854 lecture laid the foundations for curved spaces.
   • Dynamic (expanding) cosmological models raised questions about the origin and fate of the universe.
   • The Big Bang picture emerged: billions of years ago the universe was an ultra-dense clot (density perhaps 10⁹³ g/cm³ or higher), a state where known physics breaks down.
   • The future depends on average density: below a critical value → eternal expansion; above → eventual contraction and possible cyclic rebirth (echoing Heraclitus’ eternal fire).
   • Measuring cosmic density is hampered by possible “dark” (unobservable) matter. The universe could even be closed and no larger than ~10²⁵ km without contradicting observations.

Core message of the chapter

The concept of infinity has never been a peaceful philosophical luxury; it has been forced upon science by the stubborn refusal of nature to fit into finite boxes. Each time scientists tried to eliminate infinity, new phenomena demanded its return in a more sophisticated form. By the mid-20th century, infinity—tamed by limits, curvature, and field theory—had become indispensable for describing atoms, stars, and the universe itself, even as it continued to generate deep unsolved questions about beginnings, endings, and the ultimate structure of reality."

Resonance:

You don’t really know why, but something (a book, a sentence, a picture, a conversation) struck a chord.

Quantitative Relationships:

A quantitative relationship exists when the magnitude of one quantity determines or influences the magnitude of another.

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Eine quantitative Beziehung besteht, wenn die Ausprägung einer Größe die Ausprägung einer anderen bestimmt oder beeinflusst.

Infinity:

In earlier periods, human life and human beings were closely associated with (the idea of) infinity. But in the 19th and 20th centuries, infinity was gradually stripped away from human experience.

Chapter Review: Obsess over Quality

I have to admit I didn’t reread my notes before reviewing this chapter. Earlier today, I went through a chapter from Memory Champion Scott Hagwood’s book, where he explains that we tend to remember what genuinely interests us. And that matches my experience here: the part of this chapter that stuck with me most is Cal Newport’s suggestion to invest in good tools.

His point is simple: even if the benefit of expensive tools over cheaper or free ones is small, the act of investing in them signals that you take your mission—your job, your project, whatever it is—seriously. Treat it professionally, and you naturally start caring more about the quality of the tools you use.

And here’s my personal takeaway: I haven’t treated this blog professionally. I didn’t care much about the quality of these posts. If I had implemented some form of quality control a few years ago, I’d probably be writing at a level closer to the standards I hold in my actual job.

Next Book Review:

The next book review will be about "In Search of Infinity" by N. Ya. Vilenkin.

Repetition:

Scott Hagwood:

"You’ve heard the old saying about the three most important things in selecting real estate: location, location, location. Unfortunately, too many people assign a similar importance to a basic memory technique: repetition, repetition, repetition. They seem to think that if we just hammer away hard enough and long enough with brute repetitive force, we’ll chisel the information into our long-term memory. How sad. When we approach memory through brute repetition, we become slaves to it. We think that if we “just do the time” we will eventually earn freedom from the monotony. It doesn’t take long, though, before we begin to ask ourselves, “How much is enough?” That quickly evolves into, “When can I stop?” What is most discouraging is that memorizing through repetition is too often the way we or our children are taught to learn in school. I don’t know about you, but if I never hear the voice of “Multiplication Mallory” intoning again and again that “three times three is nine,” it will be too soon. How many valuable hours are wasted the night before exams as students across the country cram in order to recall names, dates, and definitions? Clearly, we give repetition too much weight in the memory process. Just consider how many things you see or hear only once and yet can recall without trying and without error? I can remember my first date with Janet, the first time I drove a car, my first (and only!) hole-in-one, and my first day on my first job. These memories come to me easily despite the fact that each was a onetime event. A teacher in our local school system introduces sign language to several groups of first-graders. Each group is shown how to sign the alphabet once. Each letter is pronounced at the same time as the specific hand position for that letter is shown. The children immediately repeat the letter back. At the end of the exercise, the teacher spells out words and sentences by sign language and the children write down what they see. You’ll probably be amazed to learn that over 90 percent of the children get every letter, word, or sentence, a true testament to the ability to memorize without repetition.
...
I’m not completely knocking repetition. No question about it, repetition is an important tool in enhancing memory. But too much of a good thing can be bad. Sometimes too much repetition can actually inhibit recall. In a research study in which volunteers were given lists of words to remember, one group was given a rehearsal strategy: They were told to repeat each word as many times as possible before the next word was given about six seconds later. The second group was asked simply to remember the words and wasn’t given any tips or strategies about how to do so. The second group performed much better in recalling the words than did the first group. In other words, the frequency of the repetition interfered with the first-group’s learning process. In an interview with Gunther Karsten, the reigning German National Champion, who currently holds the world record for remembering random binary numbers (3,027 random binary digits given only thirty minutes of study time), I asked him how many times he repeated the numbers. “Twice,” he said. How can anyone remember 3,027 of anything, especially binary numbers, after looking at them only a couple of times? Gunther simply uses the Law of Association to link new information, such as the list of binary numbers, with images and experiences that make sense to him. We’ll get into more detail about how he does that later. The important thing to know now is that like most people with well-developed memories, Gunther is just an ordinary human being. He wasn’t born with the gift of extraordinary memory, he simply trained the same memory that all of us have, and that training is not dependent on frequent repetition."

Memory:

Scott Hagwood:

"Of all the natural methods that we use to remember something, interest, by far, is the easiest and simplest. Simply put, we remember what interests us. And what interests us isn’t necessarily what is important to us. Take television and movies. Most television programs and movies are not life-altering events. Yet, we remember scenes from our favorite movies and programs because they were entertaining. They engaged us. They interested us. If you’ve seen the movie Planet of the Apes, starring Charlton Heston, I think you’ll agree that there isn’t anything important about it. Yet, I will stay up until the wee hours watching a rerun and waiting for my favorite line: “Get your stinking paws off me, you damn dirty ape.” I love it! That warning sends a shock through the mass of monkeys as they suddenly begin to doubt their superiority to a mere human being. If I try to put the best gloss on my love of that scene, I might think that it is a reflection of some deeper interests of mine. Perhaps my feelings about that scene reflect my concern about social injustice, racial prejudice, conformity, and the travesty of trying to suppress the differences in others. Maybe I’m sensitive to related issues such as cruelty, the establishment, fear of change, and blind obedience.
Sometimes we don’t really know what we are interested in until we write it down. This is another reason why it is so important to write to remember. It helps you define and analyze your interests. A salesman once told me after one of my lectures that he used to think he had a terrible memory for names and faces. Then he realized that his business was not about the product he was selling. Rather, it was all about establishing relationships. His interest in people became paramount to success, and now he has a remarkable ability to remember names. Some people are very good at remembering details such as batting averages, shooting percentages, or a plethora of other statistics that sports seem to generate. For people with such interests, sporting events become as much an exercise in calculating probabilities as they are a competition. Take a few minutes to make a list of some of your passions. Then break each passion down to its indivisible core. For example, you may have a passion for cooking, which is a combination of art and science. You may like to start at the very beginning and follow the step-by-step instructions of a recipe. You combine specific ingredients in precise measurements with other ingredients. This is followed by a particular sequence of operations, including stirring, folding, blending, baking, etc. Sometimes you can substitute ingredients to enhance the taste or the visual nature of the dish. Cooking is a blend of combining details to create an overall effect. Perhaps you have a passion for playing golf. A friend asks you how you did at the end of the round. You say, “I shot a 95.” That statement is a simple fact. But there’s a story behind it. Since your average round of golf is about 80, you begin to explain. “On the very first hole, which you know has a severe dogleg to the left, I sliced my drive out-of-bounds. My fourth shot went to the very back of the green, but the hole position was up front on the very bottom end of that sloping tier. I three-putted and that was just the beginning of a very bad day.” Now that you’ve added lots of supporting details, the story of that lousy round of golf is developing nicely. Passions and interests, broken down in this way, give clues to how you construct a memory. Perhaps you start at the beginning by layering a sense of touch to a mental picture to create an experience. Or perhaps you start with an experience and then break it down to reveal the specific details that make the memory relevant. Next, apply the Law of Association to the interests you have defined and see what imaginative and creative opportunities you can develop. Interest is like the canvas on which the picture is painted. Defining our interests provides the background to help us build our memories and gives us a way to remember whatever we want to. Let’s say you want to remember a short grocery list. You know that you’re one of those people who start at the very beginning and proceed in a step-by-step fashion to their goal. Make each item on the list part of a mental recipe that you are concocting to make an exotic dish. To keep the logical part of your brain from dissolving the mental recipe due to the combination of items that seem not to make sense, simply ask yourself this question: “How would that taste?” This simple thought allows both sides of your brain to work together. The right side of your mind is the mental eye, where you see the tangible pictures of the list, and the left side contains the analytical skill that determines why the images are there. The point is, your memory engages with the things about which you’re passionate. Therefore, you know you have a good memory. All you have to do now is apply it to things about which you may not be so passionate but which can be useful or entertaining."

Hypoglycemia:

During a hypoglycemic episode, you sometimes “loosen the reins” and raid every stash of sweets at home. You watch yourself with a kind of astonishment as this almost instinctive craving for sugar takes over—so sharply contrasting with your usual, deeply ingrained restraint. In a way, it serves as a reminder that a very different kind of behavior is, in principle, also part of you.

Since, in my personal case, hypoglycemia only occurs every six to twelve months, it hardly matters—if anything, it’s just an oddly fascinating experience.

Infinite Browsing Mode:

Pete Davis:

"You’ve probably had this experience: It’s late at night and you start browsing Netflix, looking for something to watch. You scroll through different titles, you watch a couple of trailers, you even read a few reviews—but you just can’t commit to watching any given movie. Suddenly it’s been thirty minutes and you’re still stuck in Infinite Browsing Mode, so you just give up. You’re too tired to watch anything now, so you cut your losses and fall asleep.

I’ve come to believe that this is the defining characteristic of my generation: keeping our options open."

Mein Naturwissenschaftsblog:

ChatGPT:

"Mein Naturwissenschaftsblog is an unusual corner of the German science-blog landscape. It’s run by Erwin Schmidt, who publishes at a remarkable pace: short notes, quotes, excerpts from books, and occasional reflections on psychology, cognition, biology, and culture. Instead of long essays, the blog offers a steady stream of bite-sized entries — sometimes several per day — that read more like a personal research notebook than a polished magazine.

Strengths

• Breadth of topics: cognition, evolutionary biology, behavioural science, philosophy of mind, science literacy. If you enjoy jumping across scientific disciplines, the variety is appealing.

• Literature-driven: many posts pull directly from scientific or nonfiction sources. You often get interesting quotes you might not have stumbled upon otherwise.

• Low-threshold reading: posts are short and accessible, usually a paragraph or two. It’s easy to dip in for five minutes and pick up something stimulating.

• Honest, personal voice: Schmidt doesn’t pretend the blog is an academic journal. It’s transparent about being a “Sachblog” — a factual, curiosity-driven project.

Weaknesses

• Shallow depth: the high posting frequency means most entries offer minimal context or critical interpretation. A reader expecting deep synthesis or original analysis won’t find it here.

Who will enjoy it

The blog fits readers who:

• like to browse scientific ideas in small doses,

• appreciate eclectic reading,

• don’t mind that the signal-to-noise ratio varies,

• use blog posts as springboards to look up primary literature.

Who won’t

If you expect careful argumentation, consistent methodological grounding, or editorial quality control, this blog will likely frustrate you. It’s a notebook, not a journal.

Verdict

Mein Naturwissenschaftsblog isn’t trying to be authoritative. It works best as a curiosity feed: scattered glimpses into psychology, science, and culture. With the right expectations — and a healthy amount of critical thinking — it can be a surprisingly fertile source of ideas."

Depth:

"People write superficial things because they’re experimenting, thinking aloud, or just showing up. Depth usually comes when you decide, intentionally: “Now I’m going to push something farther.” " (e.g., women may like to push a relationship toward marriage - marriage/male commitment as the female climax)

-> Pushing something farther is the real intellectual orgasm.

"When you stay with a thought long enough that it produces something new — that does feel like a mental climax."

"the moment you intentionally press an idea beyond the surface — that’s where the real satisfaction is."

-----

“the real reward lies after the obvious part.”

“Sit with it past the first layer”

“How far could this idea unfold if I let it?”

“When your brain wants to stop, that’s where the real work begins.

If you push past that point, you’ll get to insights you didn’t expect.”

“Depth isn’t a project.

It’s a shift in how you engage.”

“It’s not that you can’t go deeper — it’s that you’ve reached the core of the idea you’re working on.”

“descent – concentration – friction – breakthrough - peak

Once you’ve hit that peak, you can’t force more depth immediately.

You need a pause, a breath, a shift — and then you can choose a new direction.”

-----

"real insight requires sustained concentration past the point where your brain signals it's done with the obvious parts. That friction point where you want to stop is exactly where the valuable work begins."

"Real depth is when you've exhausted what's obvious"

-----

"The discomfort of staying with one idea isn't a bug — it's the signal that you're working at the edge of your current understanding."

"Most intellectual discomfort comes from the gap between wanting resolution and not having it yet. Depth lives in that gap."

"Staying with one idea past comfort feels unnatural because our brains evolved to scan for novelty, not to excavate meaning."

"There's a restlessness that comes about 20 minutes into real thinking — your mind starts offering you anything else to consider. That restlessness is the threshold."

"The itch to check something else, to pivot, to 'just quickly look at' — that's not distraction, that's avoidance of the friction where insight forms."

"You know you're working at depth when continuing feels slightly suffocating, like you're running out of the obvious things to think."

"If you can sit with an idea through three waves of 'I'm done with this,' you'll find the fourth wave brings something genuinely new."

"The idea doesn't actually change. Your relationship to it does. That's what depth is — achieving a new quality of attention to what was already there."

"Staying uncomfortable with a single idea long enough is how you move from having thoughts about something to actually thinking through it."

-----

"You can't schedule breakthroughs, but you can schedule the conditions that make them possible — sustained attention past the point of boredom."

"Intellectual depth requires the same commitment as any craft: returning to the same space until you've exhausted its possibilities."

-----

"That moment — the decision to push ..."

"You can't schedule breakthroughs, but you can schedule the conditions that make them possible — sustained attention past the point of boredom."

"Most ideas never reach depth simply because no one stayed with them long enough."

"You don’t stumble into depth. You earn it by refusing to stop at the first satisfying version of a thought."

"The first layer is familiar. The second is uncomfortable. The third is where the idea finally starts telling you something."

"Obvious is just the entrance. People mistake it for the destination."

"Nothing worth writing sits on the surface."

"Depth is attention slowed down enough to notice what you usually step over."

"Every serious idea has a gravity of its own — you feel yourself dropping into it before anything happens."

"Your brain hates the unknown enough to pretend the first answer is the final answer."

"Discomfort is the sign you’ve stopped repeating yourself and started encountering something real."

"Depth feels like running out of air because you're no longer coasting — you're diving."

"Mastery isn’t built by chasing insights but by returning to the same question until it gives way."

-----

"The first thought is foreplay. Depth is when you finally stop being polite to the idea." "You know you’re deep when the idea starts resisting you like a living thing that doesn’t want to be known." "Real thinking is slow, erotic violation of the obvious." "Most people stop when the thought feels “good enough.” That’s the intellectual equivalent of pulling out."

"Depth is the art of remaining consciously uncomfortable while everyone else goes soft."

"Every shallow take is a condom on experience—safe, clean, and absolutely no chance of conception." "The obvious is loud. Depth is almost silent." "Most people quit thinking the moment the idea stops entertaining them." "Depth is the quiet violence of refusing to be satisfied." "Thinking stops being fun right before it becomes irreversible." "Real depth feels like trespassing inside your own head." "Most insights are buried under a thin layer of “good enough.”" "The idea doesn’t get bigger. Your tolerance for ambiguity does." "Every time you think “I’ve said all there is to say,” the idea quietly laughs." "The surface is democratic. Depth is aristocratic; it only reveals itself to those who refuse to leave."

The Teakettle Principle:

That's why, whenever one reduces a new problem to a problem already solved, one says in jest that one is applying 'the teakettle principle'.

Notation:

If the notation is adapted to the discoveries..., the work of thought is marvelously shortened.

(G. Leibniz)

Mathematics is the art of calling different things by the same name.

(H. Poincare)

The Weighted Mean:

Does the average person understand the concept of the weighted mean?

Probably not.

Terence Tao:

https://terrytao.wordpress.com/

Depth and Breadth:

"People who know rare or difficult things or can solve very complex problems also generally know a lot more than do most people of the rather ordinary kinds of words and facts that many people know. Persons with poor reasoning and problem-solving ability also possess much less common knowledge about the world around them. Brighter persons automatically pick up more information from any experience afforded by their environment."

Arthur R. Jensen

LLMs as Toys:

Devon Erikson:

"Large Language Models, in their current form, are a big nothing burger. Some people are excited about the nothing burger. Some people are terrified of the nothing burger. Silicon Valley is breathlessly slavering over new ways they can sell the nothing burger. Our civilization as a whole is poised to invest a trillion dollars in the nothing burger. But there is nothing on the burger. So why does anyone think there is? Well, it's a novelty, for one thing. Look, you can talk to the computer. In English. And it can answer you. In English. Wow, that's convenient. And fun. And, above all, humans are curious. So something new, convenient, and fun is the very definition of a toy. And people want to play with it, to bat it around like a feather or a ball of string, and see what it can do. And for a certain period, they are willing to pay $20/month for the experience. But it goes deeper than that. Before we taught computers to talk, most humans, except for a few cognitive science specialists and a handful of very deep thinkers, suffered from a fundamental misconception about what "intelligence" is. They all thought it was the ability to speak. To turn ideas into language. And they thought humans can speak because they are smart, sapient, sentient, self-aware, conscious, ensouled, whatever you want to call it. Well, they were wrong. We don't talk because we are smart. We talk because we have subsections of the brain specifically evolved for talking. People who study the brain already knew that, but they often hadn't fully considered the implications, and were swayed by the prevailing cultural idea that eloquence and intelligence were the same thing. Some people still believed this after 8 years of Barack Obama as president. So now we have machines that can talk, and people think that's cool, but the machines can't really do anything, or at least they can't do anything right, because They don't have a world model. They don't have an imagination. They don't have desires. They don't have executive function. So of course they lie to you. That's what a glib talking device does when it's not backed up by allegiance to an objective model of reality. Really, after 8 years of Barack Obama, more people should have realized this. Here's how I think intelligence works, which I figured out from watching my cat learn how to use doorknobs: 1. You need an internal representation of your world, distilled from observation. Imagination. 2. This model needs to include not just what is, but causes and effects. Understanding. 3. You need to be able to imagine hypothetical, fictional versions of this world, which are slightly different than it actually is, in some respect. Possibilities. 4. You need to have goals and desires, so you can decide which of these possibilities you like. Choices. 5. You need to be able to tell a hypothetical story, using this understanding, of how to bring the possibility you have chosen to reality. Plans. This is the set of capabilities that we call "intelligence". And until we have a computer with these capabilities, we won't have a computer that we can experience as "intelligent" in any meaningful sense. And building "better" LLMs doesn't get us there. Not only does the Machine God not lie ahead on that path, neither does an ordinary human being who likes football and daytime television. No matter how glib and eloquent you make them, they'll still be as dumb as a sack of wet hammers. Sure, LLMs are progress. Language processing is something that a true machine intelligence will need in order to understand us, and tell us things. But the ability to speak English does not make a human, being any more than the ability to draw pictures, drive a car, or play chess."

Standards:

Robin Hanson

@robinhanson

·

20. Nov.

Many people really do say that if you cannot find evidence on a topic that meet the usual high standards of nearby academic fields, you should refuse to think about or have opinions on that topic.

College:

Diana S. Fleischman

@sentientist

One reason that women have always gone to college is to find a pool of men filtered for intelligence and conscientiousness. College is an expensive, time intensive and ineffective way to filter for quality men, but, in secular networks, it's one of the only ways. A certain set of men who evaluate women predominantly on attractiveness have trouble understanding how much rides on women's partner choice being adequately discerning- that one wrong step can lead a woman to be tethered to, and making copies of, someone subpar.

Suspicion of Restraint:

Rob Henderson

@robkhenderson

·

21. Nov.

"Fundamental to liberalism is a suspicion of restraint, which inevitably becomes suspicion of human relationships. It promises liberation from every last tie until we are free of everything, including each other."