A Hamiltonian system is a way of describing motion where position and momentum evolve together as one coupled system.
The plot shows an energy landscape in phase space, with the motion of the system traced directly on top of it and projected onto the underlying phase portrait.
#HamiltonianSystems #PhaseSpace #PhysicsSimulation #DynamicalSystems #MathematicalPhysics
A Stanford psychologist spent 4 years proving that the simple act of walking generates 60% more creative ideas than sitting, and the experiment she designed to kill every alternative explanation is one of the most decisive findings in modern psychology.
Her name is Marily Oppezzo.
She got the idea for the study while walking with her advisor at Stanford to discuss her thesis topic, and the paper she eventually published in the Journal of Experimental Psychology in 2014 is sharp enough that it should have ended the seated meeting on the day it came out.
She ran 4 experiments on 176 people. Same person tested twice. Once sitting, once walking. The creativity tasks were the standard ones psychologists have used for decades to measure how good a brain is at generating novel useful ideas.
The result was almost too clean to publish.
81% of participants in the first experiment produced more creative ideas while walking than while sitting. In the second experiment, 88%. In the third, 100%. Every single person walked into a more creative version of themselves.
On average, people generated 60% more novel useful ideas the moment their legs started moving.
The skeptical question is the obvious one. Maybe it was the fresh air. Maybe it was the scenery passing by. Maybe it was the change of environment doing the work, not the walking itself.
Oppezzo killed every one of those explanations with one experimental decision.
She put people on a treadmill facing a blank wall. No scenery. No fresh air. No environmental change. Just legs moving in place while staring at white drywall. The 60% boost held.
Then she ran the experiment that closed the case completely. She took participants outside in two conditions. Half of them walked through a Stanford courtyard. The other half were pushed through the exact same courtyard in a wheelchair. Same outdoor stimulation. Same scenery passing at the same speed. The only difference was whether the legs were moving.
The walkers produced dramatically more novel high-quality ideas than the wheelchair group. The outdoors did almost nothing on its own. The walking did everything.
This is the part of the study that hit hardest when I read it the first time.
She also tested the opposite kind of thinking. Convergent thinking. The kind where there is one right answer and you have to narrow down to it.
Word puzzles where 3 words share a hidden fourth word that connects them. The seated participants did slightly better on these. Walkers got slightly worse.
Walking is not a general intelligence enhancer. It does one specific thing. It opens up the divergent search inside your brain. The part that generates options. The part that produces unexpected connections. The part that takes a problem and finds five ways into it instead of one.
When you need to converge on the single right answer, sit down. When you need to find the answer in the first place, get up.
The mechanism is now well understood. Walking selectively activates what neuroscientists call the default mode network, the system inside your brain that runs when you are not consciously focused on anything. The DMN is where mind-wandering happens. Where memories cross-reference each other. Where ideas that have been sitting in separate folders inside your head finally bump into each other.
When you sit at a desk and force yourself to concentrate, you suppress the DMN. When you walk at a natural pace, the executive part of your brain gets just busy enough handling the walking that the DMN comes online and starts doing the work that focus was blocking.
The most useful finding in the entire paper is the one almost nobody quotes.
The boost did not turn off the moment people stopped walking. Participants who walked first and then sat back down stayed elevated. Their next round of seated creativity work was still significantly better than people who had been sitting the whole time. The rest lingered for at least several minutes after the legs stopped moving.
You do not need to do creative work while walking. You need to walk before the creative work. The brain holds the state.
The history of this is the part that should haunt anyone who still does meetings in chairs.
Charles Darwin built a gravel loop behind his house in Kent called the Sandwalk and walked it 3 times a day for the rest of his life. The theory of evolution was developed one lap at a time on that path.
Nietzsche walked up to 10 hours a day during the years he wrote his most important books and openly said the work was conceived on his feet.
Beethoven composed for the morning and walked for 5 hours every afternoon with a pencil in his pocket for when something landed.
Kahneman said the best thinking of his Nobel Prize-winning career happened on leisurely walks with Amos Tversky. Steve Jobs refused to take important conversations sitting down. He held them on foot.
Every one of them was using the system Oppezzo would not measure until 2014. They just did not know what to call it.
The question worth sitting with is the one almost nobody asks.
Every meeting you have ever attended sitting around a table was a meeting held at a fraction of the brain power that was actually available to the people in the room. Every brainstorm that got stuck inside a conference room. Every problem you tried to solve at a desk and gave up on. Every idea you could not quite get to.
The intervention is the easiest one in modern science. No supplement. No app. No subscription. No training program. Just a pair of legs and 15 minutes.
The Stanford lab proved it. The philosophers knew it. The neuroscience explains it.
And almost everyone reading this is still trying to think their way out of problems sitting completely still.
New blackboard lecture w @reinerpope
How do chips actually work – starting with basic logic gates, and working up to why GPUs, TPUs, FPGAs, and the human brain each look the way they do.
0:00:00 – Building a multiply-accumulate from logic gates
0:16:20 – Muxes and the cost of data movement
0:25:59 – How systolic arrays work
0:39:00 – Clock cycles and pipeline registers
0:51:40 – FPGAs vs ASICs
1:03:14 – Cache vs scratchpad
1:07:16 – Why CPU cores are much bigger than GPU cores
1:11:49 – Brains vs chips
1:15:22 – A GPU is just a bunch of tiny TPUs
Look up Dwarkesh Podcast on YouTube/Spotify/etc to watch. Enjoy!
A Norwegian neuroscientist spent 20 years proving that the act of writing by hand changes the human brain in ways typing physically cannot, and almost nobody outside her field has read the paper.
Her name is Audrey van der Meer.
She runs a brain research lab in Trondheim, and the paper that closed the argument was published in 2024 in a journal called Frontiers in Psychology. The finding is brutal enough that it should have changed every classroom on Earth.
The experiment was simple. She recruited 36 university students and put each one in a cap with 256 sensors pressed against their scalp to record brain activity. Words flashed on a screen one at a time.
Sometimes the students wrote the word by hand on a touchscreen using a digital pen, and sometimes they typed the same word on a keyboard. Every neural response was recorded for the full five seconds the word stayed on screen.
Then her team looked at the part of the data most researchers had ignored for years, which is how different parts of the brain were communicating with each other during the task.
When the students wrote by hand, the brain lit up everywhere at once.
The regions responsible for memory, sensory integration, and the encoding of new information were all firing together in a coordinated pattern that spread across the entire cortex. The whole network was awake and connected.
When the same students typed the same word, that pattern collapsed almost completely.
Most of the brain went quiet, and the connections between regions that had been alive seconds earlier were nowhere to be found on the EEG.
Same word, same brain, same person, and two completely different neurological events.
The reason turned out to be something nobody had really paid attention to before her work. Writing by hand is not one motion but a sequence of thousands of tiny micro-movements coordinated with your eyes in real time, where each letter is a different shape that requires the brain to solve a slightly different spatial problem.
Your fingers, wrist, vision, and the parts of your brain that track position in space are all working together to produce one letter, then the next, then the next.
Typing throws all of that away. Every key on a keyboard requires the exact same finger motion regardless of which letter you are pressing, which means the brain has almost nothing to integrate and almost no problem to solve.
Van der Meer said it plainly in her interviews.
Pressing the same key with the same finger over and over does not stimulate the brain in any meaningful way, and she pointed out something that should scare every parent who handed their kid an iPad.
Children who learn to read and write on tablets often cannot tell letters like b and d apart, because they have never physically felt with their bodies what it takes to actually produce those letters on a page.
A decade before her, two researchers at Princeton ran the same fight using a completely different method and ended up at the same answer. Pam Mueller and Daniel Oppenheimer tested 327 students across three experiments, where half took notes on laptops with the internet disabled and half took notes by hand, before testing everyone on what they actually understood from the lectures they had watched.
The handwriting group won by a wide margin on every question that required real understanding rather than surface recall.
The reason was hiding in the transcripts of what the two groups had actually written down.
The laptop students typed almost word for word, capturing more total content but processing almost none of it as they went, while the handwriting students physically could not write fast enough to transcribe a lecture in real time, which forced them to listen carefully, decide what actually mattered, and put it in their own words on the page.
That single act of choosing what to keep was the learning itself, and the keyboard had quietly skipped the choosing and skipped the learning along with it.
Two studies. Two countries. Same answer.
Handwriting makes the brain work. Typing lets it coast.
Every note you have ever typed instead of written went into your brain through a thinner pipe. Every meeting, every book highlight, every idea you captured on your phone instead of on paper was processed at half depth.
You did not forget those things because your memory is bad. You forgot them because typing never woke the part of the brain that would have made them stick.
The fix is the thing your grandmother already knew.
Pick up a pen. Write the thing down. The slower road is the faster one.
A Stanford neuroscientist published a paper a few years ago that quietly answered one of the oldest questions in human history, and almost nobody outside his field has heard of it.
The question is why we dream. Not what dreams mean. Why they exist at all. Why your brain spends a third of its sleep hallucinating images instead of just resting like every other organ in your body.
His name is David Eagleman.
He runs a lab at Stanford. The paper is called "The Defensive Activation Theory", and the moment you read it the explanation collapses every other theory you have ever been taught about dreams.
Freud said dreams were repressed desires. He was guessing. He had no brain scans. He had no electrodes. He had a couch and a notebook and a century of credibility that nobody has been able to fully scrub off the subject since.
Modern neuroscience replaced him with the memory "consolidation theory". The idea that dreams are your brain sorting through the day, filing things away, deciding what to keep. That story is partially true. Sleep does consolidate memory. But it does not explain the single strangest thing about dreams, which is that they are almost entirely visual.
You do not dream in pure sound. You do not dream in taste. You do not dream in smell. You dream in pictures. Vivid, detailed, often impossible pictures that activate the back of your brain so hard a scientist scanning you would think your eyes were wide open.
Eagleman started from one fact almost nobody outside neuroscience knows. The brain is territorial. Every region holds its turf through constant electrical activity. The moment a region goes quiet, its neighbors start invading. They take the silent territory and reassign it to themselves.
This is called "cortical takeover", and it is not slow. It is not a long process measured in years. In experiments where adults are blindfolded, the visual cortex starts processing touch and sound within an hour. One hour of darkness, and the territory is already being annexed.
In congenitally blind people, the visual cortex is fully repurposed. It runs language. It runs hearing. It runs touch. The hardware never went unused. It was just reassigned to whoever showed up first.
Now sit with the implication of that for a second.
Every night, when you close your eyes and fall asleep, the sun has set. The planet has rotated. The visual cortex, which takes up roughly a third of your entire cortex, is suddenly receiving zero input. For eight hours. Every single night. For your entire life. And evolution has shaped your brain inside a planet that has been spinning into darkness for billions of years.
If cortical takeover happens in an hour, the visual cortex should have been lost a long time ago. Stolen by hearing. Stolen by touch. Reassigned by morning. Humans should have evolved into a species whose vision works fine during the day and then degrades every time the sun goes down because the territory keeps getting renegotiated overnight.
But that did not happen. Vision works the moment you open your eyes. Which means something is defending the territory while you sleep.
Eagleman's claim is that dreams are that defense.
Every 90 minutes through the night, a precise burst of activity fires from the brainstem into the visual cortex. Pontine-geniculate-occipital waves. PGO for short. They are anatomically aimed. They are not general arousal.
They are a targeted volley of signal launched directly at the back of the brain where vision lives. The cortex lights up as if it is receiving real images, and you experience that artificial activation as a dream. The bizarre narrative your conscious mind invents around it later is just your brain trying to make sense of the noise.
The dream is not the point. The dream is the side effect. The point is keeping the territory occupied.
The evidence for this is the part that should haunt you.
Newborns spend roughly 50% of their sleep in REM. Adults spend twenty. Old adults spend fifteen. The amount of dreaming you do tracks almost perfectly with how plastic your brain is. Newborns have the most plastic brains on earth. Their visual cortex is in the highest danger of being overrun by neighboring senses while it develops.
So evolution gave them an enormous defense budget. As you age, your brain becomes less plastic, the takeover risk drops, and the defense system scales down accordingly.
Eagleman and his co-author ran the same correlation across twenty-five primate species. The more plastic a species' brain, the higher the proportion of REM sleep. The relationship held across the entire primate family tree. Plasticity and dreaming move together. They are two halves of the same evolutionary equation.
A species that ranks higher on flexibility and learning also dreams more. A species that is born ready to walk and survive dreams less. Plasticity is the asset. Dreaming is the insurance premium.
And the prediction the theory makes is the one that quietly closes the case.
Of all your senses, only one is disadvantaged by darkness. You can still hear in the dark. You can still feel in the dark. You can still smelll and taste in the dark. The only sense that depends on light is vision. Which is exactly the sense your dreams are made of. The defense system is targeted at the only territory that is actually vulnerable while you sleep.
Memory consolidation is real. Emotional processing is real. Your brain does do those things at night. But Eagleman's argument is that those functions piggyback on a much older system whose original job was simpler and more brutal. Keep the lights on inside the visual cortex while the planet is dark, or lose it.
For thousands of years, people have asked what dreams mean. Prophets wrote about them. Poets wrote about them. Freud built a discipline on them. None of them had access to the actual answer, which is that dreams may not mean anything in the symbolic sense at all.
They may be the visible flicker of a defense system running in the background, the way a screen saver protects a monitor by keeping the pixels moving even when nobody is looking.
The strangest thing about the theory is how cleanly it explains why dreams feel so real. Your visual cortex cannot tell the difference between a PGO wave and an actual photon. It is the same hardware lighting up the same way. The cortex does its job. It builds an image. Your conscious mind, half-awake, wraps a story around it and calls it a dream.
You are not seeing your subconscious tonight. You are watching your brain defend a piece of itself from being stolen.
Every animal that has ever closed its eyes on this planet has done the same thing.
Right now Kherson is under massive bombardment. FPV attacks have doubled to 600 EVERY DAY. Glide bombs are constant. Entire neighbourhoods are turning to rubble.
Russians are hunting innocent civilians on the streets. Women, children, war crimes in plain sight. They are trying to completely destroy the city. International coverage is almost zero & the situation is catastrophic.
In this report, I embed with a drone patrol that are the city’s first line of defence. What I witnessed was brutality on an industrial scale.
If Russia isn’t stopped, this will spread and Kherson will be a blueprint for cities across Europe in the future. Europe stopped violence like this before in WW2 and it can do it again.
Please watch and share my latest:
Did a very different format with @reinerpope – a blackboard lecture where he walks through how frontier LLMs are trained and served.
It's shocking how much you can deduce about what the labs are doing from a handful of equations, public API prices, and some chalk.
It’s a bit technical, but I encourage you to hang in there - it’s really worth it.
There are less than a handful of people who understand the full stack of AI, from chip design to model architecture, as well as Reiner. It was a real delight to learn from him.
Recommend watching this one on YouTube so you can see the chalkboard.
0:00:00 – How batch size affects token cost and speed
0:31:59 – How MoE models are laid out across GPU racks
0:47:02 – How pipeline parallelism spreads model layers across racks
1:03:27 – Why Ilya said, “As we now know, pipelining is not wise.”
1:18:49 – Because of RL, models may be 100x over-trained beyond Chinchilla-optimal
1:32:52 – Deducing long context memory costs from API pricing
2:03:52 – Convergent evolution between neural nets and cryptography
🚨 The creator of Claude Code just shared a full walkthrough on how to actually use it the right way.
30 minutes. Free. Straight from the person who built it.
Watch the workshop and save it for later.
You’ll likely get more practical value from this than from most expensive coding courses online.
Most people are only scratching the surface of what Claude Code can do.
Then check out the guide below.
I often get accused of having a “pro-Ukraine bias.” Here’s the truth. I am biased.
I’m biased towards freedom, democracy, & human rights. That’s what Ukraine represents right now.
When you document war crimes, you don’t pretend there are “two sides” for balance. You show what is happening. One side is the aggressor. One side is the victim.
If that offends you, you’re morally bankrupt.
👉 “Chronic treatment with DAS (found in garlic 🧄) freshly added to the diet weekly revealed geroprotective effects, since it extended lifespan and improved metabolic homeostasis, locomotor function, and relevant cognitive parameters in wild-type male mice fed with an STD. DAS extended lifespan by 11.4%, which almost doubles the effects of metformin (5.8% increase),53 which is considered the leading candidate among experimental anti-aging interventions to be tested in humans.”
Reflection: When I wrote Lifespan, I hoped it might become a classic, something that would last and shape how people think about aging
I didn’t expect it to become part of the zeitgeist
What has surprised me most is the level of engagement. Readers don’t just absorb the ideas, they question long-held assumptions about aging and health
It’s been a genuine joy to have people come up to me and say the book transformed their lives and even their families
Lifespan also revealed to readers something important: there’s a gap between what scientists understand about aging and what the public hears from mainstream and social media
Lifespan, the book and the show, helped narrow that gap, at least a little. That’s why I’m restarting the show in the coming weeks.
And as I deal with another mainstream media story tonight, one reminder: if you want to change the world, never give up - even when the system tries its best to trip you up and bring you down
Onward!
Today, Hungary had the highest voting turnout since the fall of communism.
An Orban party Mayor defected & voted for the opposition. All across the country, people told me they are done with corruption and Russian influence.
Tonight is likely the end of Orban
Orban supporters and party members were genuinely shocked last night. They didn’t expect this. Musk is now saying it’s Soros fault. In reality, this is what happens after 16 years of corruption & Putinism.
If thought were independent of language, we wouldn’t have any use for language, because the whole point of language is to convey ideas. So it’s not independent, but it’s not the same thing as language. We know it’s not the same thing for many reasons. One of them is: how would children learn language to begin with if they were incapable of thinking until they had language? The way that language acquisition has to work is that children have some understanding of the world, of the objects around them, of the intentions of the people that they interact with, and they map them onto the sequences of sounds and gestures that they perceive.
Also, we know that there are many forms of thought that are not linguistic, such as visual imagery, spatial cognition, and mental maps, all of which are specialties of Professor Tversky, who I’m sure will enlighten us about those. Even when it comes to the content of language, what we take away after the words have faded is the gist of language, not the words themselves. Within a few seconds after I stop speaking, or a few minutes after you’ve read something, you probably could not reproduce a single sentence verbatim, but hopefully you would come away with the content, the meaning, the gist. And one of the most robust findings in our field, cognitive psychology, is that long-term memory for gist is far more robust than memory for text itself.
We know from studies of the brain that there are networks of language in the brain that are not the same as the parts of the brain that light up when people are thinking visually, thinking spatially, or thinking in terms of motion. Again, to go back to one of Professor Tversky’s specializations, we can imagine tying a shoe; we can imagine diving off a board. We have auditory imagery—a song can run through our head—and there are probably other forms of thought that we don’t even have names for. We also know that we sometimes struggle to put our thoughts into words. We write down a sentence, and we realize, no, that’s not what I meant, and rewrite it until the sentence comes out right.
Full @IAI_TV video: https://t.co/UOJh7hZWlA
A major new paper reframes aging as a systems failure of epigenetic information. Not wear and tear but a software problem. This is what the Information Theory of Aging predicts and, if correct, means aging is reversible.
Let's dive in... 🧵
When you get fitter, you release more BDNF after exercise.
Improvements in VO₂ max after 12 weeks of training were associated with greater changes in post-exercise BDNF levels (even though resting BDNF didn't change). And the more VO₂ max improved, the higher BDNF rose after exercise.
Post-exercise BDNF was also associated with changes in prefrontal cortex activity during cognitively demanding tasks.
This illustrates a neat relationship between aerobic fitness, BDNF, and cognitive function!
Success doesn’t truly make us happier. Why?
Our neurobiology is wired for progress, not arrival. The dopamine system rewards the pursuit. Once a goal is reached, the brain resets and the target moves.
It’s what @arthurbrooks calls the “striver’s curse.” You work relentlessly toward a goal believing it will bring lasting satisfaction, but when you get there, the feeling fades quickly. The trap is thinking the answer is more (more success, money, weight loss, etc).
A better framework: Satisfaction = what you have ÷ what you want.
Most people try to increase the numerator. But the more powerful lever is reducing the denominator (wanting less).
I recommend creatine to nearly everyone. But here are my caveats:
1. Make sure it's creatine monohydrate - this is the form that's most well-studied and effective. You don't need a "fancy" form.
2. Beware of gummies. If you use them, make sure you're getting one that's been third-party tested and contains the stated amount of creatine (many brands do not).
3. Look for an an NSF certification. This will help avoid heavy metals and other contaminants you don't want.
Clip is from my recent appearance on @JordanHarbinger show!
Scientists put kids through 100 hours of reading, then scanned their brains. New wiring had physically grown inside the language regions. Communication between brain areas sped up by a factor of 10. Kids who didn't read showed zero change.
That was a 2009 Carnegie Mellon study. It gets wilder.
In 2013, Emory University scanned 19 students every morning for 19 straight days while they read one novel chapter each night. Mornings after reading, the brain areas responsible for understanding other people's emotions lit up with new connections. So did the region that processes physical sensation. Their brains were simulating what the characters felt, as if it were happening to them. Those changes stuck around for 5 days after they finished the book.
Now flip to scrolling. A massive review published in Psychological Bulletin last September pulled together 71 studies covering 98,299 people. Heavy short-form video use (TikTok, Reels, Shorts) showed a clear pattern: worse attention, weaker self-control, and more anxiety. Consistent across teenagers and adults, across every platform tested. Oxford didn't name "brain rot" its 2024 Word of the Year for nothing.
A 2024 brain wave study found that people hooked on short-form video had weaker activity in the front of the brain, the part that controls focus and impulse control. Separate brain scans showed the same thing: heavy scrollers had less activation in the exact regions that deep reading strengthens.
UCLA neuroscientist Maryanne Wolf has been studying this for decades. Humans were never born to read. There's no gene for it. Reading is something we invented, and it hijacked neurons that were originally meant for recognizing faces. Over time, it built entirely new brain circuits connecting language, vision, and emotion. But those circuits only survive if you use them. Stop reading, and they fade. Wolf's conclusion is simple: screens built for speed produce a speed-wired brain. Books built for depth produce a depth-wired brain.
One honest caveat: most of these studies are snapshots, not long-term tracking. People who already struggle to focus might just prefer short videos. But the same pattern showing up across nearly 100,000 people is hard to shrug off.
The tweet repeats the line seven times. The research backs it up with brain scans, EEG data, and white-matter imaging across tens of thousands of people.