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You and Your Research, a talk by Richard Hamming
You and Your Research, a talk by Richard Hamming
I will talk mainly about science because that is what I have studied. But so far as I know, and I've been told by others, much of what I say applies to many fields. Outstanding work is characterized very much the same way in most fields, but I will confine myself to science.
I spoke earlier about planting acorns so that oaks will grow. You can't always know exactly where to be, but you can keep active in places where something might happen. And even if you believe that great science is a matter of luck, you can stand on a mountain top where lightning strikes; you don't have to hide in the valley where you're safe.
Most great scientists know many important problems. They have something between 10 and 20 important problems for which they are looking for an attack. And when they see a new idea come up, one hears them say ``Well that bears on this problem.'' They drop all the other things and get after it.
The great scientists, when an opportunity opens up, get after it and they pursue it. They drop all other things. They get rid of other things and they get after an idea because they had already thought the thing through. Their minds are prepared; they see the opportunity and they go after it. Now of course lots of times it doesn't work out, but you don't have to hit many of them to do some great science. It's kind of easy. One of the chief tricks is to live a long time!
He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important. Now I cannot prove the cause and effect sequence because you might say, ``The closed door is symbolic of a closed mind.'' I don't know. But I can say there is a pretty good correlation between those who work with the doors open and those who ultimately do important things, although people who work with doors closed often work harder.
You should do your job in such a fashion that others can build on top of it, so they will indeed say, ``Yes, I've stood on so and so's shoulders and I saw further.'' The essence of science is cumulative. By changing a problem slightly you can often do great work rather than merely good work. Instead of attacking isolated problems, I made the resolution that I would never again solve an isolated problem except as characteristic of a class.
by altering the problem, by looking at the thing differently, you can make a great deal of difference in your final productivity because you can either do it in such a fashion that people can indeed build on what you've done, or you can do it in such a fashion that the next person has to essentially duplicate again what you've done. It isn't just a matter of the job, it's the way you write the report, the way you write the paper, the whole attitude. It's just as easy to do a broad, general job as one very special case. And it's much more satisfying and rewarding!
it is not sufficient to do a job, you have to sell it. `Selling' to a scientist is an awkward thing to do. It's very ugly; you shouldn't have to do it. The world is supposed to be waiting, and when you do something great, they should rush out and welcome it. But the fact is everyone is busy with their own work. You must present it so well that they will set aside what they are doing, look at what you've done, read it, and come back and say, ``Yes, that was good.'' I suggest that when you open a journal, as you turn the pages, you ask why you read some articles and not others. You had better write your report so when it is published in the Physical Review, or wherever else you want it, as the readers are turning the pages they won't just turn your pages but they will stop and read yours. If they don't stop and read it, you won't get credit.
I think it is very definitely worth the struggle to try and do first-class work because the truth is, the value is in the struggle more than it is in the result. The struggle to make something of yourself seems to be worthwhile in itself. The success and fame are sort of dividends, in my opinion.
He had his personality defect of wanting total control and was not willing to recognize that you need the support of the system. You find this happening again and again; good scientists will fight the system rather than learn to work with the system and take advantage of all the system has to offer. It has a lot, if you learn how to use it. It takes patience, but you can learn how to use the system pretty well, and you can learn how to get around it. After all, if you want a decision `No', you just go to your boss and get a `No' easy. If you want to do something, don't ask, do it. Present him with an accomplished fact. Don't give him a chance to tell you `No'. But if you want a `No', it's easy to get a `No'.
Amusement, yes, anger, no. Anger is misdirected. You should follow and cooperate rather than struggle against the system all the time.
I found out many times, like a cornered rat in a real trap, I was surprisingly capable. I have found that it paid to say, ``Oh yes, I'll get the answer for you Tuesday,'' not having any idea how to do it. By Sunday night I was really hard thinking on how I was going to deliver by Tuesday. I often put my pride on the line and sometimes I failed, but as I said, like a cornered rat I'm surprised how often I did a good job. I think you need to learn to use yourself. I think you need to know how to convert a situation from one view to another which would increase the chance of success.
I do go in to strictly talk to somebody and say, ``Look, I think there has to be something here. Here's what I think I see ...'' and then begin talking back and forth. But you want to pick capable people. To use another analogy, you know the idea called the `critical mass.' If you have enough stuff you have critical mass. There is also the idea I used to call `sound absorbers'. When you get too many sound absorbers, you give out an idea and they merely say, ``Yes, yes, yes.'' What you want to do is get that critical mass in action; ``Yes, that reminds me of so and so,'' or, ``Have you thought about that or this?'' When you talk to other people, you want to get rid of those sound absorbers who are nice people but merely say, ``Oh yes,'' and to find those who will stimulate you right back.
On surrounding yourself with people who provoke meaningful progress
I believed, in my early days, that you should spend at least as much time in the polish and presentation as you did in the original research. Now at least 50% of the time must go for the presentation. It's a big, big number.
Luck favors a prepared mind; luck favors a prepared person. It is not guaranteed; I don't guarantee success as being absolutely certain. I'd say luck changes the odds, but there is some definite control on the part of the individual.
If you read all the time what other people have done you will think the way they thought. If you want to think new thoughts that are different, then do what a lot of creative people do - get the problem reasonably clear and then refuse to look at any answers until you've thought the problem through carefully how you would do it, how you could slightly change the problem to be the correct one. So yes, you need to keep up. You need to keep up more to find out what the problems are than to read to find the solutions. The reading is necessary to know what is going on and what is possible. But reading to get the solutions does not seem to be the way to do great research. So I'll give you two answers. You read; but it is not the amount, it is the way you read that counts.
Avoiding excessive reading before thinking
your dreams are, to a fair extent, a reworking of the experiences of the day. If you are deeply immersed and committed to a topic, day after day after day, your subconscious has nothing to do but work on your problem. And so you wake up one morning, or on some afternoon, and there's the answer.
#dreams , subconscious processing
#advice#career#philosophy#writing#research#work/productivity#stem#science#talks#transcript#academic
·blog.samaltman.com·
You and Your Research, a talk by Richard Hamming
Data Laced with History: Causal Trees & Operational CRDTs
Data Laced with History: Causal Trees & Operational CRDTs
After mulling over my bullet points, it occurred to me that the network problems I was dealing with—background cloud sync, editing across multiple devices, real-time collaboration, offline support, and reconciliation of distant or conflicting revisions—were all pointing to the same question: was it possible to design a system where any two revisions of the same document could be merged deterministically and sensibly without requiring user intervention?
It’s what happened after sync that was troubling. On encountering a merge conflict, you’d be thrown into a busy conversation between the network, model, persistence, and UI layers just to get back into a consistent state. The data couldn’t be left alone to live its peaceful, functional life: every concurrent edit immediately became a cross-architectural matter.
I kept several questions in mind while doing my analysis. Could a given technique be generalized to arbitrary and novel data types? Did the technique pass the PhD Test? And was it possible to use the technique in an architecture with smart clients and dumb servers?
Concurrent edits are sibling branches. Subtrees are runs of characters. By the nature of reverse timestamp+UUID sort, sibling subtrees are sorted in the order of their head operations.
This is the underlying premise of the Causal Tree. In contrast to all the other CRDTs I’d been looking into, the design presented in Victor Grishchenko’s brilliant paper was simultaneously clean, performant, and consequential. Instead of dense layers of theory and labyrinthine data structures, everything was centered around the idea of atomic, immutable, metadata-tagged, and causally-linked operations, stored in low-level data structures and directly usable as the data they represented.
I’m going to be calling this new breed of CRDTs operational replicated data types—partly to avoid confusion with the exiting term “operation-based CRDTs” (or CmRDTs), and partly because “replicated data type” (RDT) seems to be gaining popularity over “CRDT” and the term can be expanded to “ORDT” without impinging on any existing terminology.
Much like Causal Trees, ORDTs are assembled out of atomic, immutable, uniquely-identified and timestamped “operations” which are arranged in a basic container structure. (For clarity, I’m going to be referring to this container as the structured log of the ORDT.) Each operation represents an atomic change to the data while simultaneously functioning as the unit of data resultant from that action. This crucial event–data duality means that an ORDT can be understood as either a conventional data structure in which each unit of data has been augmented with event metadata; or alternatively, as an event log of atomic actions ordered to resemble its output data structure for ease of execution
To implement a custom data type as a CT, you first have to “atomize” it, or decompose it into a set of basic operations, then figure out how to link those operations such that a mostly linear traversal of the CT will produce your output data. (In other words, make the structure analogous to a one- or two-pass parsable format.)
OT and CRDT papers often cite 50ms as the threshold at which people start to notice latency in their text editors. Therefore, any code we might want to run on a CT—including merge, initialization, and serialization/deserialization—has to fall within this range. Except for trivial cases, this precludes O(n2) or slower complexity: a 10,000 word article at 0.01ms per character would take 7 hours to process! The essential CT functions have to be O(nlogn) at the very worst.
Of course, CRDTs aren’t without their difficulties. For instance, a CRDT-based document will always be “live”, even when offline. If a user inadvertently revises the same CRDT-based document on two offline devices, they won’t see the familiar pick-a-revision dialog on reconnection: both documents will happily merge and retain any duplicate changes. (With ORDTs, this can be fixed after the fact by filtering changes by device, but the user will still have to learn to treat their documents with a bit more caution.) In fully decentralized contexts, malicious users will have a lot of power to irrevocably screw up the data without any possibility of a rollback, and encryption schemes, permission models, and custom protocols may have to be deployed to guard against this. In terms of performance and storage, CRDTs contain a lot of metadata and require smart and performant peers, whereas centralized architectures are inherently more resource-efficient and only demand the bare minimum of their clients. You’d be hard-pressed to use CRDTs in data-heavy scenarios such as screen sharing or video editing. You also won’t necessarily be able to layer them on top of existing infrastructure without significant refactoring.
Perhaps a CRDT-based text editor will never quite be as fast or as bandwidth-efficient as Google Docs, for such is the power of centralization. But in exchange for a totally decentralized computing future? A world full of devices that control their own data and freely collaborate with one another? Data-centric code that’s entirely free from network concerns? I’d say: it’s surely worth a shot!
#local-first#technical#academic#science#math#research#tech#collaboration#swift#backend#data structures
·archagon.net·
Data Laced with History: Causal Trees & Operational CRDTs
Psilocybin desynchronizes the human brain - Nature
Psilocybin desynchronizes the human brain - Nature

Claude summary: This research provides new insights into how psilocybin affects large-scale brain activity and connectivity. The key finding is that psilocybin causes widespread desynchronization of brain activity, particularly in association cortex areas. This desynchronization correlates with the intensity of subjective psychedelic experiences and may underlie both the acute effects and potential therapeutic benefits of psilocybin. The desynchronization of brain networks may allow for increased flexibility and plasticity, potentially explaining both the acute psychedelic experience and longer-term therapeutic effects.

Psilocybin acutely caused profound and widespread brain FC changes (Fig. 1a) across most of the cerebral cortex (P < 0.05 based on two-sided linear mixed-effects (LME) model and permutation testing), but most prominent in association networks
Across psilocybin sessions and participants, FC change tracked with the intensity of the subjective experience (Fig. 1f and Extended Data Fig. 4).
#drugs/psychedelics#study#academic#science#neuroscience#research#cognition
·nature.com·
Psilocybin desynchronizes the human brain - Nature
The Only Reason to Explore Space
The Only Reason to Explore Space

Claude summary: > This article argues that the only enduring justification for space exploration is its potential to fundamentally transform human civilization and our understanding of ourselves. The author traces the history of space exploration, from the mystical beliefs of early rocket pioneers to the geopolitical motivations of the Space Race, highlighting how current economic, scientific, and military rationales fall short of sustaining long-term commitment. The author contends that achieving interstellar civilization will require unprecedented organizational efforts and societal commitment, likely necessitating institutions akin to governments or religions. Ultimately, the piece suggests that only a society that embraces the pursuit of interstellar civilization as its central legitimating project may succeed in this monumental endeavor, framing space exploration not as an inevitable outcome of progress, but as a deliberate choice to follow a "golden path to a destiny among the stars."

#sci-fi#history#future#philosophy#space#govt#tech#culture#science
·palladiummag.com·
The Only Reason to Explore Space
Toxic Gaslighting: How 3M Executives Convinced a Scientist the Forever Chemicals She Found in Human Blood Were Safe
Toxic Gaslighting: How 3M Executives Convinced a Scientist the Forever Chemicals She Found in Human Blood Were Safe
Johnson asked Hansen to figure out whether the lab had made a mistake. Detecting trace levels of chemicals was her specialty: She had recently written a doctoral dissertation about tiny particles in the atmosphere.
Hansen didn’t want to share her results until she was certain that they were correct, so she and her team spent several weeks analyzing more blood, often in time-consuming overnight tests. All the samples appeared to be contaminated. When Hansen used a more precise method, liquid chromatography, the results left little doubt that the chemical in the Red Cross blood was PFOS. Hansen now felt obligated to update her boss. Johnson was a towering, bearded man, and she liked him: He seemed to trust her expertise, and he found something to laugh about in most conversations. But, when she shared her findings, his response was cryptic. “This changes everything,” he said. Before she could ask him what he meant, he went into his office and closed the door.
In the middle of this testing, Johnson suddenly announced that he would be taking early retirement. After he packed up his office and left, Hansen felt adrift. She was so new to corporate life that her office clothes — pleated pants and dress shirts — still felt like a costume. Johnson had always guided her research, and he hadn’t told Hansen what she should do next. She reminded herself of what he had said — that the chemical wasn’t harmful in factory workers. But she couldn’t be sure that it was harmless.
Hansen’s bosses never told her that PFOS was toxic. In the weeks after Johnson left 3M, however, she felt that she was under a new level of scrutiny. One of her superiors suggested that her equipment might be contaminated, so she cleaned the mass spectrometer and then the entire lab. Her results didn’t change. Another encouraged her to repeatedly analyze her syringes, bags and test tubes, in case they had tainted the blood. (They had not.) Her managers were less concerned about PFOS, it seemed to Hansen, than about the chance that she was wrong.
Hansen doubted herself. She was 28 and had only recently earned her Ph.D. But she continued her experiments, if only to respond to the questions of her managers. 3M bought three additional mass spectrometers, which each cost more than a car, and Hansen used them to test more blood samples. In late 1997, her new boss, Bacon, even had her fly out to the company that manufactured the machines, so that she could repeat her tests there. She studied the blood of hundreds of people from more than a dozen blood banks in various states. Each sample contained PFOS. The chemical seemed to be everywhere.
After the war, 3M hired some Manhattan Project chemists and began mass-producing chains of carbon atoms bonded to fluorine atoms. The resulting chemicals proved to be astonishingly versatile, in part because they resist oil, water and heat. They are also incredibly long-lasting, earning them the moniker “forever chemicals.”
One afternoon in 1998, a trim 3M epidemiologist named Geary Olsen arrived with several vials of blood and asked her to test them. The next morning, she read the results to him and several colleagues — positive for PFOS. As Hansen remembers it, Olsen looked triumphant. “Those samples came from my horse,” he said — and his horse certainly wasn’t eating at McDonald’s or trotting on Scotchgarded carpets. Hansen felt that he was trying to humiliate her. (Olsen did not respond to requests for comment.) What Hansen wanted to know was how PFOS was making its way into animals.
PFOS, a man-made chemical produced by her employer, really was in human blood, practically everywhere. Hansen’s team found it in Swedish blood samples from 1957 and 1971. After that, her lab analyzed blood that had been collected before 3M created PFOS. It tested negative. Apparently, fluorochemicals had entered human blood after the company started selling products that contained them. They had leached out of 3M’s sprays, coatings and factories — and into all of us.
Almost as soon as Hansen placed her first transparency on the projector, the attendees began interrogating her: Why did she do this research? Who directed her to do it? Whom did she inform of the results? The executives seemed to view her diligence as a betrayal: Her data could be damaging to the company. She remembers defending herself, mentioning Newmark’s similar work in the ’70s and trying, unsuccessfully, to direct the conversation back to her research. While the executives talked over her, Hansen noticed that DeSimone’s eyes had closed and that his chin was resting on his dress shirt. The CEO appeared to have fallen asleep. (DeSimone died in 2017. A company spokesperson did not answer my questions about the meeting.)
In 2002, when 3M announced that it would be replacing PFOS with another fluorochemical, PFBS, Hansen knew that it, too, would remain in the environment indefinitely. Still, she decided not to involve herself. She skipped over articles about the chemicals in scientific journals and newspapers, where they were starting to be linked to possible developmental, immune system and liver problems.
In the 2016 book “Secrecy at Work,” two management theorists, Jana Costas and Christopher Grey, argue that there is nothing inherently wrong or harmful about keeping secrets. Trade secrets, for example, are protected by federal and state law on the grounds that they promote innovation and contribute to the economy. The authors draw on a large body of sociological research to illustrate the many ways that information can be concealed. An organization can compartmentalize a secret by slicing it into smaller components, preventing any one person from piecing together the whole. Managers who don’t want to disclose sensitive information may employ “stone-faced silence.” Secret-keepers can form a kind of tribe, dependent on one another’s continued discretion; in this way, even the existence of a secret can be kept secret. Such techniques become pernicious, Costas and Grey write, when a company keeps a dark secret, a secret about wrongdoing.
Hansen’s superiors had given her the same explanation that they gave journalists, she finally said — that factory workers were fine, so people with lower levels would be, too. Her specialty was the detection of chemicals, not their harms. “You’ve got literally the medical director of 3M saying, ‘We studied this, there are no effects,’” she told me. “I wasn’t about to challenge that.” Her income had helped to support a family of five. Perhaps, I wondered aloud, she hadn’t really wanted to know whether her company was poisoning the public.
Jim Johnson, who is now an 81-year-old widower, lives with several dogs in a pale-yellow house in North Dakota. When I first called him, he said that he had begun researching PFOS in the ’70s. “I did a lot of the very original work on it,” he told me. He said that when he saw the chemical’s structure he understood “within 20 minutes” that it would not break down in nature. Shortly thereafter, one of his experiments revealed that PFOS was binding to proteins in the body, causing the chemical to accumulate over time. He told me that he also looked for PFOS in an informal test of blood from the general population, around the late ’70s, and was not surprised when he found it there.
Johnson said that he eventually tired of arguing with the few colleagues with whom he could speak openly about PFOS. “It was time,” he said. So he hired an outside lab to look for the chemical in the blood of 3M workers, knowing that it would also test blood bank samples for comparison — the first domino in a chain that would ultimately take the compound off the market. Oddly, he compared the head of the lab to a vending machine. “He gave me what I paid for,” Johnson said. “I knew what would happen.” Then Johnson tasked Hansen with something that he had long avoided: going beyond his initial experiments and meticulously documenting the chemical’s ubiquity. While Hansen took the heat, he took early retirement. Johnson described Hansen as though she were a vending machine, too. “She did what she was supposed to do with the tools I left her,” he said.
I pointed out that Hansen had suffered professionally and personally, and that she now feels those experiences tainted her career. “I didn’t say I was a nice guy,” Johnson replied, and laughed. After four hours, we were nearing the bottom of our bottomless coffees.
Average levels of PFOS are falling, but nearly all people have at least one forever chemical in their blood, according to the Centers for Disease Control and Prevention. “When you have a contaminated site, you can clean it up,” Elsie Sunderland, an environmental chemist at Harvard University, told me. “When you ubiquitously introduce a toxicant at a global scale, so that it’s detectable in everyone ... we’re reducing public health on an incredibly large scale.” Once everyone’s blood is contaminated, there is no control group with which to compare, making it difficult to establish responsibility.
At least 45% of U.S. tap water is estimated to contain one or more forever chemicals, and one drinking water expert told me that the cost of removing them all would likely reach $100 billion.
n 2022, 3M said that it would stop making PFAS and would “work to discontinue the use of PFAS across its product portfolio,” by the end of 2025 — a pledge that it called “another example of how we are positioning 3M for continued sustainable growth.” But it acknowledged that more than 16,000 of its products still contained PFAS.
#environment#sustainability#expose#profile#business#ethics#science#science/materials#health/forever chemicals
·propublica.org·
Toxic Gaslighting: How 3M Executives Convinced a Scientist the Forever Chemicals She Found in Human Blood Were Safe
Can technology’s ‘zoomers’ outrun the ‘doomers’?
Can technology’s ‘zoomers’ outrun the ‘doomers’?
Hassabis pointed to the example of AlphaFold, DeepMind’s machine-learning system that had predicted the structures of 200mn proteins, creating an invaluable resource for medical researchers. Previously, it had taken one PhD student up to five years to model just one protein structure. DeepMind calculated that AlphaFold had therefore saved the equivalent of almost 1bn years of research time.
DeepMind, and others, are also using AI to create new materials, discover new drugs, solve mathematical conjectures, forecast the weather more accurately and improve the efficiency of experimental nuclear fusion reactors. Researchers have been using AI to expand emerging scientific fields, such as bioacoustics, that could one day enable us to understand and communicate with other species, such as whales, elephants and bats.
#trends#tech#ai#startups#culture#science
·ft.com·
Can technology’s ‘zoomers’ outrun the ‘doomers’?
In an ugly world, vaccines are a beautiful gift worth honouring
In an ugly world, vaccines are a beautiful gift worth honouring
nice words on vaccines
Vaccines are not only immensely useful; they also embody something beautifully human in their combination of care and communication. Vaccines do not trick the immune system, as is sometimes said; they educate and train it. As a resource of good public health, they allow doctors to whisper words of warning into the cells of their patients. In an age short of trust, this intimacy between government policy and an individual’s immune system is easily misconstrued as a threat. But vaccines are not conspiracies or tools of control: they are molecular loving-kindness.
#history#healthcare#science
·economist.com·
In an ugly world, vaccines are a beautiful gift worth honouring
The challenge of 'renewable' energy.
The challenge of 'renewable' energy.
Secure energy is prerequisite to the prosperity that lifts people out of poverty.  At the same time, we want to protect the environment while providing this secure energy.  Achieving that will require competing interests to play together in the “radical middle” where conflicting goals collide around energy, the economy and the environment.
More than half of what we consume in the world today is made in countries that use coal to make it. So, we sometimes close our ears and eyes, and say, “We’re green. Just keep making our stuff over there and we’ll buy it on Amazon and have it delivered to our door one small thing at a time.” This is not good for the climate.
Emissions in Asia go into the one unique atmosphere that we all share, and by not reducing our consumption of products, we are simply moving the source of those emissions far away.
Kale is healthy, but it is not dense calorically, so you would have to eat a lot of it. Beef is dense with calories to sustain life, but too much of it is not all that healthy. Wind and solar and hydroelectric power are like kale, ideal if only you could live on the energy it provides.  Coal and oil and natural gas and nuclear power are like cow, less benign, but energy dense. Not just a little denser. Several hundred times denser.
#sustainability#energy#science#tech#climate
·readtangle.com·
The challenge of 'renewable' energy.
Apple Vision
Apple Vision
Apple Vision is technically a VR device that experientially is an AR device, and it’s one of those solutions that, once you have experienced it, is so obviously the correct implementation that it’s hard to believe there was ever any other possible approach to the general concept of computerized glasses.
the Vision is taking that captured image, processing it, and displaying it in front of your eyes in around 4 milliseconds.
Real-time operating systems are used in embedded systems for applications with critical functionality, like a car, for example: it’s ok to have an infotainment system that sometimes hangs or even crashes, in exchange for more flexibility and capability, but the software that actually operates the vehicle has to be reliable and unfailingly fast. This is, in broad strokes, one way to think about how visionOS works: while the user experience is a time-sharing operating system that is indeed a variation of iOS, and runs on the M2 chip, there is a subsystem that primarily operates the R1 chip that is real-time; this means that even if visionOS hangs or crashes, the outside world is still rendered under that magic 12 milliseconds.
I’ll be honest: what this looked like to me was a divorced dad, alone at home with his Vision Pro, perhaps because his wife was irritated at the extent to which he got lost in his own virtual experience.
#visionOS#tech#science#future#xr#ar#companies/apple
·stratechery.com·
Apple Vision
Kill Math
Kill Math
If I had to guess why "math reform" is misinterpreted as "math education reform", I would speculate that school is the only contact that most people have had with math. Like school-physics or school-chemistry, math is seen as a subject that is taught, not a tool that is used. People don't actually use math-beyond-arithmetic in their lives, just like they don't use the inverse-square law or the periodic table.
Teach the current mathematical notation and methods any way you want -- they will still be unusable. They are unusable in the same way that any bad user interface is unusable -- they don't show users what they need to see, they don't match how users want to think, they don't show users what actions they can take.
They are unusable in the same way that the UNIX command line is unusable for the vast majority of people. There have been many proposals for how the general public can make more powerful use of computers, but nobody is suggesting we should teach everyone to use the command line. The good proposals are the opposite of that -- design better interfaces, more accessible applications, higher-level abstractions. Represent things visually and tangibly. And so it should be with math. Mathematics, as currently practiced, is a command line. We need a better interface.
Anything that remains abstract (in the sense of not concrete) is hard to think about... I think that mathematicians are those who succeed in figuring out how to think concretely about things that are abstract, so that they aren't abstract anymore. And I believe that mathematical thinking encompasses the skill of learning to think of an abstract thing concretely, often using multiple representations – this is part of how to think about more things as "things". So rather than avoiding abstraction, I think it's important to absorb it, and concretize the abstract... One way to concretize something abstract might be to show an instance of it alongside something that is already concrete.
The mathematical modeling tools we employ at once extend and limit our ability to conceive the world. Limitations of mathematics are evident in the fact that the analytic geometry that provides the foundation for classical mechanics is insufficient for General Relativity. This should alert one to the possibility of other conceptual limits in the mathematics used by physicists.
#academic#ux#ui#math#science
·worrydream.com·
Kill Math