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Graph theory

Anthony Bonato

29,374 subscribers

2,028,975 Aufrufe • vor 1 Jahr •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

21 Kommentare

Profilbild von TheRealVerbz (Jason Verbelli)

TheRealVerbz (Jason Verbelli)vor 1 Jahr

Now to the extreme:

Profilbild von Андрей

Андрейvor 1 Jahr

You mean group theory?

Profilbild von Aghiles Kheffache

Aghiles Kheffachevor 1 Jahr

I think this is group theory

Profilbild von $olaire

$olairevor 1 Jahr

The slice moves make sense but the regular face moves are complicated on this graph. During a regular face move, some nodes (but not all) have to take a path traced by two different circles.

Profilbild von Jero

Jerovor 1 Jahr

Now do for language!

Profilbild von JESUS

JESUSvor 1 Jahr

XyzT plots

Profilbild von π

πvor 1 Jahr

knot theory

Profilbild von Ian Adams

Ian Adamsvor 1 Jahr

This is next level cool thank you for sharing Anthony I also subscribe check out some of my art on media

Profilbild von I.T.

I.T.vor 1 Jahr

instead of sheeps, I'm counting group permutations

Profilbild von bubba

bubbavor 1 Jahr

Imma need an explanation or a github link this is too cool

Profilbild von Shub

Shubvor 1 Jahr

Beautiful

Profilbild von Dauntless

Dauntlessvor 1 Jahr

now I get it!!!!!

Profilbild von LVC 📚

LVC 📚vor 1 Jahr

Thanks.

Profilbild von Gleiton Franco

Gleiton Francovor 1 Jahr

😯‼️

Profilbild von Pavlos Papageorgiou

Pavlos Papageorgiouvor 1 Jahr

I think at some point they marketed a toy inspired by this but it only had 2 or 3 loops.

Profilbild von K3ith.AI

K3ith.AIvor 1 Jahr

Isn’t this group theory🤔🤨😉

Profilbild von Sheesh 🤠

Sheesh 🤠vor 1 Jahr

What!? I just felt my brain unlock a new of spatial awareness for the first time

Profilbild von Steven Walter

Steven Waltervor 1 Jahr

That of just cool

Profilbild von Totoro

Totorovor 1 Jahr

I think it is not graph theory but group theory.

Profilbild von π

πvor 1 Jahr

why the Stroop test literally doesn't work on the quantum mechanic department studying quantum light based plasmonic gravity

Profilbild von peer of eyes

peer of eyesvor 1 Jahr

I'd rather call binocular vision, stereopsis of renewed kind. The LHS, yes, will be new to targeted eyes unlike the all-too-famous RHS. But the spectacle is of the equivalence evidenced by their parallel motion, while "graph theory" strictly hypes just the LHS, however disputbly

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Claude Code creator, Boris Cherny: "Forget everything you learned about computer science theory, now you just explain to the model what you need and it does the rest." 32 minutes of the head of Claude Code showing exactly how he builds now. He gave Claude one prompt two weeks ago and it's still running, spawning thousands of agents on its own. The people winning right now aren't writing more code, they're building loops that run without them. Watch it, then go deeper with the graph engineering guide that combines agents and loops below.

Claude Code creator, Boris Cherny: "Forget everything you learned about computer science theory, now you just explain to the model what you need and it does the rest." 32 minutes of the head of Claude Code showing exactly how he builds now. He gave Claude one prompt two weeks ago and it's still running, spawning thousands of agents on its own. The people winning right now aren't writing more code, they're building loops that run without them. Watch it, then go deeper with the graph engineering guide that combines agents and loops below.

Anatoli Kopadze

47,071 Aufrufe • vor 1 Monat

How were humans able to recognize that Newton's laws of motion govern both the flight of a bird and the motion of a pendulum? This ability to identify the same mathematical patterns across vastly different contexts lies at the heart of scientific discovery—whether studying the aerodynamics of bird wings or designing the blades of a wind turbine. Yet, AI systems often struggle to discern these deep structural similarities. 💡The key may lie in mathematical isomorphisms—patterns that preserve their relationships regardless of context. For example, the same principles of fluid dynamics apply to blood flowing through arteries and air streaming over an airplane wing, or the motion of a molecule. This raises a fundamental question in artificial intelligence: how can we enable machines to understand the world through these invariant structures rather than surface features? 🚀Our work introduces Graph-Aware Isomorphic Attention, improving how Transformers recognize patterns across domains. Drawing from category theory, models can learn unifying structural principles that describe phenomena as diverse as the hierarchical assembly of spider silk proteins and the compositional patterns in music. By making these deep similarities explicit, Isomorphic Attention enables AI to reason more like humans do—seeing past surface differences to grasp fundamental patterns that unite seemingly disparate fields. Through this lens, AI systems can learn and generalize, moving beyond superficial pattern matching to true structural understanding. The implications span from scientific discovery to engineering design, offering a new approach to artificial intelligence that mirrors how humans grasp the underlying unity of natural phenomena. Some key insights include: 1️⃣ Graph Isomorphism Neural Networks (GINs): GIN-style aggregation ensures structurally distinct graphs map to distinct embeddings, improving generalization and avoiding relational pattern collapse. 2️⃣ Category Theory Perspective: Transformers as functors preserve structural relationships. Sparse-GIN refines attention into sparse adjacency matrices, unifying domain knowledge across tasks. 3️⃣ Information Bottleneck & Sparsification: Sparsity reduces overfitting by filtering irrelevant edges, aligning with natural systems. Sparse-GIN outperforms dense attention by focusing on crucial connections. 4️⃣ Hierarchical Representation Learning: GIN-Attention captures multiscale patterns, mirroring structures like spider silk. Nested GINs model local and global dependencies across fields. 5️⃣ Practical Impact: Sparse-GIN enables domain-specific fine-tuning atop pre-trained Transformer foundation models, reducing the need for full retraining. Other impacts: ✅Real-World Relevance: Whether we are looking at protein structures, designing new materials, or working on social network analytics, graph-aware Transformers can capture subtle relational patterns traditional architectures may miss. ✅The juncture of graph isomorphism theory, category theory, and sparsification, these GIN-Transformers step beyond sequential modeling to tackle the relational nature of complex data. #Transformers #GraphNeuralNetworks #AI #MachineLearning #Isomorphism #CategoryTheory #ArtificialIntelligence #DeepLearning Link to paper & code in response ⤵️

How were humans able to recognize that Newton's laws of motion govern both the flight of a bird and the motion of a pendulum? This ability to identify the same mathematical patterns across vastly different contexts lies at the heart of scientific discovery—whether studying the aerodynamics of bird wings or designing the blades of a wind turbine. Yet, AI systems often struggle to discern these deep structural similarities. 💡The key may lie in mathematical isomorphisms—patterns that preserve their relationships regardless of context. For example, the same principles of fluid dynamics apply to blood flowing through arteries and air streaming over an airplane wing, or the motion of a molecule. This raises a fundamental question in artificial intelligence: how can we enable machines to understand the world through these invariant structures rather than surface features? 🚀Our work introduces Graph-Aware Isomorphic Attention, improving how Transformers recognize patterns across domains. Drawing from category theory, models can learn unifying structural principles that describe phenomena as diverse as the hierarchical assembly of spider silk proteins and the compositional patterns in music. By making these deep similarities explicit, Isomorphic Attention enables AI to reason more like humans do—seeing past surface differences to grasp fundamental patterns that unite seemingly disparate fields. Through this lens, AI systems can learn and generalize, moving beyond superficial pattern matching to true structural understanding. The implications span from scientific discovery to engineering design, offering a new approach to artificial intelligence that mirrors how humans grasp the underlying unity of natural phenomena. Some key insights include: 1️⃣ Graph Isomorphism Neural Networks (GINs): GIN-style aggregation ensures structurally distinct graphs map to distinct embeddings, improving generalization and avoiding relational pattern collapse. 2️⃣ Category Theory Perspective: Transformers as functors preserve structural relationships. Sparse-GIN refines attention into sparse adjacency matrices, unifying domain knowledge across tasks. 3️⃣ Information Bottleneck & Sparsification: Sparsity reduces overfitting by filtering irrelevant edges, aligning with natural systems. Sparse-GIN outperforms dense attention by focusing on crucial connections. 4️⃣ Hierarchical Representation Learning: GIN-Attention captures multiscale patterns, mirroring structures like spider silk. Nested GINs model local and global dependencies across fields. 5️⃣ Practical Impact: Sparse-GIN enables domain-specific fine-tuning atop pre-trained Transformer foundation models, reducing the need for full retraining. Other impacts: ✅Real-World Relevance: Whether we are looking at protein structures, designing new materials, or working on social network analytics, graph-aware Transformers can capture subtle relational patterns traditional architectures may miss. ✅The juncture of graph isomorphism theory, category theory, and sparsification, these GIN-Transformers step beyond sequential modeling to tackle the relational nature of complex data. #Transformers #GraphNeuralNetworks #AI #MachineLearning #Isomorphism #CategoryTheory #ArtificialIntelligence #DeepLearning Link to paper & code in response ⤵️

Markus J. Buehler

19,416 Aufrufe • vor 1 Jahr

Holy shit... One month before Andrej Karpathy dropped the “LLM Wiki” idea… someone had already built it. Not theory. Not hype. A working system. LLMs today restart from zero every time. No memory. No evolution. No learning. That’s broken. Most people use CLAUDE.md / AGENTS.md → Manual updates → Easy to forget → Knowledge gets lost That’s not intelligence. That’s a notepad. So I built dynamic memory for LLMs: • Learns automatically • Stores without manual effort • Weakens irrelevant data over time • Strengthens what actually matters Before the “LLM Wiki” idea went viral, this already had: • Brain-like decay/boost memory • Smart deduplication (no noise) • Experience tracking per tech • Cross-referenced knowledge graph • Loss-proof backups • Auto-grouped tool sessions Then I added: • memory_audit (clean + optimize memory) • Memory injection directly into tools Now this isn’t just a concept. It’s a live system that turns LLMs from stateless tools → evolving intelligence. Using it daily: → ~5K tokens → Zero manual work → Memory that actually compounds Link in comments. RT & Bookmark — this will be standard soon.

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Nainsi Dwivedi

15,726 Aufrufe • vor 4 Monaten

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Deyao Zhu

362,388 Aufrufe • vor 2 Monaten

Scrolling insta and I saw this video by a French girl, and it reminds of a frequent complaint of expats in Australia: it’s actually really hard to make local Australian friends there You see this complaint all over expat forums, even white Brits talk about it, so it’s not even primarily a racial or religious thing In my opinion it’s because Australia is a culture which ranks very high in the “cliquey-ness” extremity. Australia often catches people off guard, because they can’t comprehend how people can be so friendly and outgoing, but also very closed socially, and it’s because they confuse the qualities of extroversion and warmth with actual social-group openness There is a graph I made around this theory (based on the 4 square political compass chart) that I use to roughly plot the primary social dynamic of cities, and I think it can be helpful in selecting a city that best suits your situation and social style. Will do another post about it

Scrolling insta and I saw this video by a French girl, and it reminds of a frequent complaint of expats in Australia: it’s actually really hard to make local Australian friends there You see this complaint all over expat forums, even white Brits talk about it, so it’s not even primarily a racial or religious thing In my opinion it’s because Australia is a culture which ranks very high in the “cliquey-ness” extremity. Australia often catches people off guard, because they can’t comprehend how people can be so friendly and outgoing, but also very closed socially, and it’s because they confuse the qualities of extroversion and warmth with actual social-group openness There is a graph I made around this theory (based on the 4 square political compass chart) that I use to roughly plot the primary social dynamic of cities, and I think it can be helpful in selecting a city that best suits your situation and social style. Will do another post about it

nomadgeist

54,535 Aufrufe • vor 4 Monaten

University of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: Daniel Litt Lisha

University of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: Daniel Litt Lisha

a16z

138,341 Aufrufe • vor 4 Tagen

In recent days, multiple Erdős problems have been solved by GPT-5.2 Pro, with solutions accepted by Terence Tao. This is not a gimmick—it's a qualitative shift. Erdős problems lie at the core of additive combinatorics, extremal graph theory, and probabilistic methods—problems that resist brute force and demand structural insight. Many have endured decades of expert scrutiny. Acceptance matters more than authorship. Tao doesn't rubber-stamp ideas; he rigorously tests logic, generality, and novelty. If a proof clears that hurdle, the system didn't merely recombine known lemmas—it explored a true mathematical search space. This means AI has crossed a threshold: from assisting mathematics to participating in it by proposing nontrivial arguments, uncovering hidden structures, and resolving problems humans value—without a predefined solution path. Importantly, this doesn't diminish human mathematicians. It reshapes the field's topology. Just as symbolic algebra systems amplified rather than replaced math, AI now seems poised to expand the frontier itself. If these claims hold, recent days may mark the lift-off for AI-driven science: not flashy demos, but quiet validation by the world's toughest referees. We should remain skeptical, careful, and precise—yet honest about the implications. Something fundamental may have changed. Here's a five-minute video with Terry explaining these problems and meeting the man himself:

In recent days, multiple Erdős problems have been solved by GPT-5.2 Pro, with solutions accepted by Terence Tao. This is not a gimmick—it's a qualitative shift. Erdős problems lie at the core of additive combinatorics, extremal graph theory, and probabilistic methods—problems that resist brute force and demand structural insight. Many have endured decades of expert scrutiny. Acceptance matters more than authorship. Tao doesn't rubber-stamp ideas; he rigorously tests logic, generality, and novelty. If a proof clears that hurdle, the system didn't merely recombine known lemmas—it explored a true mathematical search space. This means AI has crossed a threshold: from assisting mathematics to participating in it by proposing nontrivial arguments, uncovering hidden structures, and resolving problems humans value—without a predefined solution path. Importantly, this doesn't diminish human mathematicians. It reshapes the field's topology. Just as symbolic algebra systems amplified rather than replaced math, AI now seems poised to expand the frontier itself. If these claims hold, recent days may mark the lift-off for AI-driven science: not flashy demos, but quiet validation by the world's toughest referees. We should remain skeptical, careful, and precise—yet honest about the implications. Something fundamental may have changed. Here's a five-minute video with Terry explaining these problems and meeting the man himself:

Prof. Brian Keating

104,865 Aufrufe • vor 7 Monaten

[wip] growing organisms using hypergraph rewriting I'm exploring generating organisms using string forces and I was wondering about which class of algorithms could be used to generalize the growth of such structures. I wanted a system which can produce a wide variety of outputs, while allowing for stable and controlled growth. That's when I thought about Stephen Wolfram (yes again) Physics Project, which proposes to explore a solution to the fundamental theory of physics using a hypergraph rewriting system ( TLDR; Growth of graphs using simple permutation rules. It's similar to cellular automata but for graphs. Could be what I'm looking for. I started to experiment with this system to grow my organisms, and it's definitely a promising approach! Below is a video of the following rules applied to an initial {{0,0},{0,0}} graph: rand() {{x,y},{x,w},{y,w},{z,w}} : {{x,y},{x,z}}->{{x,w},{y,w},{z,w}} There's a lot of areas to improve this exploration, notably: - localization of rules (instead of applying a same rule to the whole system, let each node have its own rules) - spawn control rules (when a new node is created, a rule can define which rules will be applied to such node) - mutation rules (rules which alter rules of adjacent nodes) - conditional rules (many rules can be attached to a node, the one being executed subject to localized conditions) Super exciting, will certainly be the basis of my next project.

[wip] growing organisms using hypergraph rewriting I'm exploring generating organisms using string forces and I was wondering about which class of algorithms could be used to generalize the growth of such structures. I wanted a system which can produce a wide variety of outputs, while allowing for stable and controlled growth. That's when I thought about Stephen Wolfram (yes again) Physics Project, which proposes to explore a solution to the fundamental theory of physics using a hypergraph rewriting system ( TLDR; Growth of graphs using simple permutation rules. It's similar to cellular automata but for graphs. Could be what I'm looking for. I started to experiment with this system to grow my organisms, and it's definitely a promising approach! Below is a video of the following rules applied to an initial {{0,0},{0,0}} graph: rand() {{x,y},{x,w},{y,w},{z,w}} : {{x,y},{x,z}}->{{x,w},{y,w},{z,w}} There's a lot of areas to improve this exploration, notably: - localization of rules (instead of applying a same rule to the whole system, let each node have its own rules) - spawn control rules (when a new node is created, a rule can define which rules will be applied to such node) - mutation rules (rules which alter rules of adjacent nodes) - conditional rules (many rules can be attached to a node, the one being executed subject to localized conditions) Super exciting, will certainly be the basis of my next project.

ciphrd

86,001 Aufrufe • vor 1 Jahr

The cognitive dissonance of the climate agenda is on full display, and it’s more alarming than many realize. A recent analysis breaks down the chilling logic presented by global climate officials. The premise: A warming planet cannot feed a growing population. The proposed "solution"? To prevent future food scarcity caused by a 2-degree temperature rise, we must deliberately sabotage our current global food supply system. Yes, you read that correctly. To avert a hypothetical future famine, we are being guided toward creating a very real one in the present. The evidence is in the policy. Look no further than the Netherlands, where a court has mandated a drastic reduction in nitrogen emissions—a move that directly targets the synthetic fertilizers responsible for feeding roughly half of the world's current population. A stark graph reveals the terrifying math: ➡️ The yellowish line shows our current reality: nearly 8 billion people fed, thanks in large part to synthetic fertilizers. ➡️ The green line shows the pre-industrial alternative: a planet that can sustainably support only about 4 billion people. The conclusion is inescapable. The stated policies of global elites would effectively halve the world's food production capacity. They are engineering the very crisis—wars over food, mass starvation—that they claim nature will inflict upon us. This isn't a conspiracy theory. It's the logical endgame of their own publicly stated plans. They are pulling the lever on a self-inflicted catastrophe, all in the name of saving us. The question now is, will we continue to watch it happen?

The cognitive dissonance of the climate agenda is on full display, and it’s more alarming than many realize. A recent analysis breaks down the chilling logic presented by global climate officials. The premise: A warming planet cannot feed a growing population. The proposed "solution"? To prevent future food scarcity caused by a 2-degree temperature rise, we must deliberately sabotage our current global food supply system. Yes, you read that correctly. To avert a hypothetical future famine, we are being guided toward creating a very real one in the present. The evidence is in the policy. Look no further than the Netherlands, where a court has mandated a drastic reduction in nitrogen emissions—a move that directly targets the synthetic fertilizers responsible for feeding roughly half of the world's current population. A stark graph reveals the terrifying math: ➡️ The yellowish line shows our current reality: nearly 8 billion people fed, thanks in large part to synthetic fertilizers. ➡️ The green line shows the pre-industrial alternative: a planet that can sustainably support only about 4 billion people. The conclusion is inescapable. The stated policies of global elites would effectively halve the world's food production capacity. They are engineering the very crisis—wars over food, mass starvation—that they claim nature will inflict upon us. This isn't a conspiracy theory. It's the logical endgame of their own publicly stated plans. They are pulling the lever on a self-inflicted catastrophe, all in the name of saving us. The question now is, will we continue to watch it happen?

Camus

15,963 Aufrufe • vor 9 Monaten

Holy shit… someone just made DSA finally click. Not static notes Not boring pseudocode Not guessing what happens in memory Real data structures — animating step-by-step — visually. It’s called Data Structure Visualizations and it lets you watch algorithms run in real time. Here’s why this is different: Instead of dumping theory, it shows execution live • nodes getting inserted • trees rotating • pointers moving • queues filling • stacks popping • graphs traversing • heaps rebalancing You literally see algorithms think. Everything is interactive: • Binary Search Trees • AVL Trees (with rotations) • Red-Black Trees • Heaps & Priority Queues • Graph BFS / DFS • Dijkstra & MST • Hash Tables • Tries • Sorting (Quick, Merge, Heap…) • Dynamic Programming No black box. Just input → steps → result Watch in real time: • AVL rotations balancing themselves • BFS exploring layer by layer • DFS diving deep then backtracking • Dijkstra relaxing edges step-by-step • Quick sort partition visually • Heap forming after each insert • Hash collisions resolving live This solves the biggest DSA problem: Most resources teach code → memorize → hope it works This shows input → execution → visualization → understanding Which means you finally understand: • why AVL rotates • how heap property maintains • how BFS differs from DFS • how Dijkstra actually updates distances • what happens during rehashing • how quicksort partitions • how trees rebalance Even better: You control everything Change values Insert nodes Run step-by-step Pause execution Replay algorithms Learning DSA becomes interactive Not passive Not confusing Not theoretical Just… visible. Perfect for: • DSA beginners • interview prep • visual learners • CS students • LeetCode prep • teaching algorithms • debugging understanding This is the kind of resource that makes trees, graphs, and sorting finally click. Link: We’re moving from reading DSA → watching DSA execute And once you can see algorithms… you stop memorizing and start understanding.

Holy shit… someone just made DSA finally click. Not static notes Not boring pseudocode Not guessing what happens in memory Real data structures — animating step-by-step — visually. It’s called Data Structure Visualizations and it lets you watch algorithms run in real time. Here’s why this is different: Instead of dumping theory, it shows execution live • nodes getting inserted • trees rotating • pointers moving • queues filling • stacks popping • graphs traversing • heaps rebalancing You literally see algorithms think. Everything is interactive: • Binary Search Trees • AVL Trees (with rotations) • Red-Black Trees • Heaps & Priority Queues • Graph BFS / DFS • Dijkstra & MST • Hash Tables • Tries • Sorting (Quick, Merge, Heap…) • Dynamic Programming No black box. Just input → steps → result Watch in real time: • AVL rotations balancing themselves • BFS exploring layer by layer • DFS diving deep then backtracking • Dijkstra relaxing edges step-by-step • Quick sort partition visually • Heap forming after each insert • Hash collisions resolving live This solves the biggest DSA problem: Most resources teach code → memorize → hope it works This shows input → execution → visualization → understanding Which means you finally understand: • why AVL rotates • how heap property maintains • how BFS differs from DFS • how Dijkstra actually updates distances • what happens during rehashing • how quicksort partitions • how trees rebalance Even better: You control everything Change values Insert nodes Run step-by-step Pause execution Replay algorithms Learning DSA becomes interactive Not passive Not confusing Not theoretical Just… visible. Perfect for: • DSA beginners • interview prep • visual learners • CS students • LeetCode prep • teaching algorithms • debugging understanding This is the kind of resource that makes trees, graphs, and sorting finally click. Link: We’re moving from reading DSA → watching DSA execute And once you can see algorithms… you stop memorizing and start understanding.

Suryansh Tiwari

14,425 Aufrufe • vor 5 Monaten

Flip a coin. Heads, your account goes up 50 percent. Tails, it goes down 40 percent. Expected value is plus 5 percent a flip, so you take the bet a hundred times. Expected value says your $10,000 becomes $1.3 million. The most likely path leaves you with $52. An MIT professor explains the entire gap in one sentence, in a free undergraduate lecture, then moves on like it was nothing. His name is John Tsitsiklis. He teaches undergraduate probability at MIT. He also proved in 1994 that Q-learning converges, the result that says the algorithm under modern reinforcement learning does not merely happen to work, it has to. INFORMS gave him the von Neumann Theory Prize for that line of work in 2018. He runs the lecture on the students for an hour. First he takes the average apart. A random variable is not a number, it is a function. A bar graph of probabilities is a PMF. Expectation is the center of gravity of that bar graph, the single point where you slide a pen underneath and the thing balances. He is slow and patient about it. By minute 35 you trust the average completely. Then he stops and says he wants to give "one general word of caution." "The average of a function of a random variable, in general, is not the same as the function of the average... in general, you can not reason on the average." Everything before that sentence was the trap. Go back to the coin. Compounding is not addition. Up 50 then down 40 is not plus 10. It is 1.5 times 0.6, which is 0.9. You are down 10 percent. Do that 50 times each way and you have 0.9 to the fiftieth power. Fifty-two dollars. So where did the $1.3 million go? It is real. It is parked at the very top of the distribution. Run the hundred flips and only about one path in seven finishes above where you started. Only about one in a hundred ever reaches that $1.3 million. Those few runs are gigantic, and they carry the average for everybody else. You will not be in them. In February 2018 that trade had a ticker. XIV, short volatility, $1.9 billion in it. It had paid on the average day for seven years. On February 5 the VIX rose 115.6 percent, the biggest one-day jump ever recorded. XIV went from $115.55 to $4.22 overnight. Credit Suisse shut the note two weeks later. Nobody in it was wrong about the average. They were wrong about which path they were standing on. The usable version: your compound return is your average return minus roughly half your variance. A system averaging 20 percent a year at 40 percent vol does not compound at 20. It compounds at 12. That missing 8 is not fees or slippage. Tsitsiklis delivers the most expensive sentence in finance, finishes the variance section, and ends with "see you on Wednesday." The lecture is free. The average is free. Knowing which path you are standing on is the trade.

Flip a coin. Heads, your account goes up 50 percent. Tails, it goes down 40 percent. Expected value is plus 5 percent a flip, so you take the bet a hundred times. Expected value says your $10,000 becomes $1.3 million. The most likely path leaves you with $52. An MIT professor explains the entire gap in one sentence, in a free undergraduate lecture, then moves on like it was nothing. His name is John Tsitsiklis. He teaches undergraduate probability at MIT. He also proved in 1994 that Q-learning converges, the result that says the algorithm under modern reinforcement learning does not merely happen to work, it has to. INFORMS gave him the von Neumann Theory Prize for that line of work in 2018. He runs the lecture on the students for an hour. First he takes the average apart. A random variable is not a number, it is a function. A bar graph of probabilities is a PMF. Expectation is the center of gravity of that bar graph, the single point where you slide a pen underneath and the thing balances. He is slow and patient about it. By minute 35 you trust the average completely. Then he stops and says he wants to give "one general word of caution." "The average of a function of a random variable, in general, is not the same as the function of the average... in general, you can not reason on the average." Everything before that sentence was the trap. Go back to the coin. Compounding is not addition. Up 50 then down 40 is not plus 10. It is 1.5 times 0.6, which is 0.9. You are down 10 percent. Do that 50 times each way and you have 0.9 to the fiftieth power. Fifty-two dollars. So where did the $1.3 million go? It is real. It is parked at the very top of the distribution. Run the hundred flips and only about one path in seven finishes above where you started. Only about one in a hundred ever reaches that $1.3 million. Those few runs are gigantic, and they carry the average for everybody else. You will not be in them. In February 2018 that trade had a ticker. XIV, short volatility, $1.9 billion in it. It had paid on the average day for seven years. On February 5 the VIX rose 115.6 percent, the biggest one-day jump ever recorded. XIV went from $115.55 to $4.22 overnight. Credit Suisse shut the note two weeks later. Nobody in it was wrong about the average. They were wrong about which path they were standing on. The usable version: your compound return is your average return minus roughly half your variance. A system averaging 20 percent a year at 40 percent vol does not compound at 20. It compounds at 12. That missing 8 is not fees or slippage. Tsitsiklis delivers the most expensive sentence in finance, finishes the variance section, and ends with "see you on Wednesday." The lecture is free. The average is free. Knowing which path you are standing on is the trade.

Veles

628,984 Aufrufe • vor 1 Monat

Millions have watched an MIT professor accidentally destroy the American sports betting industry in a free 12-lecture undergraduate poker course. MIT charges $85,000 a year to sit in that classroom. He posted every lecture on OpenCourseWare for nothing. Almost no one who has ever placed a DraftKings same-game parlay has finished all twelve. His name is Kevin Desmond. He is an MIT alum, a professional poker player, and the instructor of 15.S50 Poker Theory and Analytics, which MIT gave undergraduates college credit for taking during January of 2015. The 43-minute clip in this video is one lecture from that course, filmed at MIT that same month. The chart on the screen behind him looks like a poker graph. It is the exact math that decides whether a Wall Street quant clears $500,000 a year, whether a FanDuel bettor loses their rent money on a Sunday afternoon, and whether a Silicon Valley founder can walk into a term sheet negotiation without being taken apart in the room. Desmond compresses the mathematical foundation of every adversarial decision on earth into five ideas. Ranges. You never know your opponent's exact hand. You know a distribution of hands weighted by probability. Every FanDuel bettor picking a parlay on a hunch is playing without a range. Every retail trader guessing a competitor's next move is guessing blind. Pot odds. The equation that tells you when a call has positive expected value. Every VC term sheet and every insurance premium reduces to it. Every same-game parlay on DraftKings violates it in ways the app is legally allowed to hide from you. Expected value. Sum every outcome weighted by probability. Casinos are built on it. Poker pros live on it. Sports bettors violate it every time they chase a loss hoping for a hot Sunday. Game theory optimal. The Nash equilibrium of poker. The strategy no opponent can exploit no matter how well they read you. Quant funds pay $500,000 bonuses for one senior who can solve for it under pressure. Exploitative play. When to deviate from GTO to punish a specific mistake. What every senior desk on Wall Street does against retail order flow, every trading session, every day. Every quant fund on Wall Street runs a hiring pipeline that starts with this material. Every prop trading desk drills it into juniors before their first live session. The MIT professor who filmed the whole course posted it on OpenCourseWare for the price of an internet connection. "Every time you play a hand differently from the way you would have played it if you could see all your opponent's cards, they gain." That is David Sklansky's Fundamental Theorem of Poker. Desmond opens the course with it. It is also the exact statement of information asymmetry that every trading floor, casino, and DraftKings promo card on earth is built to exploit. The lectures are free on MIT OpenCourseWare. The problem sets are online. Every equation Desmond derives fits on one page. The math is free. The willingness to spend 43 minutes on one lecture before opening a sportsbook app, placing a parlay, or entering a negotiation is a much rarer commodity than the confidence to walk in without it.

Millions have watched an MIT professor accidentally destroy the American sports betting industry in a free 12-lecture undergraduate poker course. MIT charges $85,000 a year to sit in that classroom. He posted every lecture on OpenCourseWare for nothing. Almost no one who has ever placed a DraftKings same-game parlay has finished all twelve. His name is Kevin Desmond. He is an MIT alum, a professional poker player, and the instructor of 15.S50 Poker Theory and Analytics, which MIT gave undergraduates college credit for taking during January of 2015. The 43-minute clip in this video is one lecture from that course, filmed at MIT that same month. The chart on the screen behind him looks like a poker graph. It is the exact math that decides whether a Wall Street quant clears $500,000 a year, whether a FanDuel bettor loses their rent money on a Sunday afternoon, and whether a Silicon Valley founder can walk into a term sheet negotiation without being taken apart in the room. Desmond compresses the mathematical foundation of every adversarial decision on earth into five ideas. Ranges. You never know your opponent's exact hand. You know a distribution of hands weighted by probability. Every FanDuel bettor picking a parlay on a hunch is playing without a range. Every retail trader guessing a competitor's next move is guessing blind. Pot odds. The equation that tells you when a call has positive expected value. Every VC term sheet and every insurance premium reduces to it. Every same-game parlay on DraftKings violates it in ways the app is legally allowed to hide from you. Expected value. Sum every outcome weighted by probability. Casinos are built on it. Poker pros live on it. Sports bettors violate it every time they chase a loss hoping for a hot Sunday. Game theory optimal. The Nash equilibrium of poker. The strategy no opponent can exploit no matter how well they read you. Quant funds pay $500,000 bonuses for one senior who can solve for it under pressure. Exploitative play. When to deviate from GTO to punish a specific mistake. What every senior desk on Wall Street does against retail order flow, every trading session, every day. Every quant fund on Wall Street runs a hiring pipeline that starts with this material. Every prop trading desk drills it into juniors before their first live session. The MIT professor who filmed the whole course posted it on OpenCourseWare for the price of an internet connection. "Every time you play a hand differently from the way you would have played it if you could see all your opponent's cards, they gain." That is David Sklansky's Fundamental Theorem of Poker. Desmond opens the course with it. It is also the exact statement of information asymmetry that every trading floor, casino, and DraftKings promo card on earth is built to exploit. The lectures are free on MIT OpenCourseWare. The problem sets are online. Every equation Desmond derives fits on one page. The math is free. The willingness to spend 43 minutes on one lecture before opening a sportsbook app, placing a parlay, or entering a negotiation is a much rarer commodity than the confidence to walk in without it.

Lumen

57,583 Aufrufe • vor 18 Tagen

Stanford professor Judy Fan went on stage at MIT and broke down why humans are so good at making the invisible visible... And why AI hasn't actually learned to "see" the way we do. It completely changes how you think about Human Intelligence v/s Artificial Intelligence: 1. Nature never gave us straight lines or sharp corners. The number line, the coordinate plane, even basic geometry are all human inventions. We created tools that do not exist in nature simply because we needed a way to think more clearly. 2. The coordinate system Descartes invented solved a problem that had stumped mathematicians for centuries, doubling the volume of a cube. Once invented, this tool became so indispensable that virtually every math curriculum on Earth still depends on it. 3. Humans have been doing this for at least 30,000 to 80,000 years. The story of human progress is inseparable from the story of marking up our environment, from cave walls to Galileo's telescope to Feynman diagrams of particles we will never see with our own eyes. 4. Every major scientific breakthrough relied on a visual tool that made something invisible visible. Darwin needed side-by-side illustrations of finches to see variation that was otherwise too subtle to notice. Cajal needed detailed drawings of neurons under a microscope to map how the nervous system was wired. 5. Fan's research group studies something deceptively simple: how people decide what to put into a drawing and what to leave out. When two people played a drawing game, sketchers used far more detail when the target object had close competitors than when it stood alone, all the way down to using fewer strokes and less time when more detail was not necessary. 6. People are not just copying what they see. They are making constant judgment calls about what level of detail actually serves the goal of communication, and they do this naturally without ever being taught the theory behind it. 7. There is a real difference between drawing something so someone can identify it and drawing something so someone can understand how it works. In one study, participants drew explanatory diagrams that emphasized moving, causal parts of a machine while depictive drawings emphasized background and overall appearance, even though both were drawing the exact same object. 8. Explanatory drawings were genuinely better at helping someone figure out how to operate a machine, but worse at helping someone identify which machine it actually was. You cannot optimize a single drawing for both goals at once. Communication always involves tradeoffs. 9. AI vision models trained on photographs generalize surprisingly well to simple, sparse sketches, suggesting that resemblance based recognition is not just a story we tell ourselves. It is something modern neural networks can replicate with real accuracy. 10. But there remains a large, measurable gap between how confidently AI models recognize sketches and how confidently humans do, even when both groups answer the same questions about the same images. Humans are simply far more reliable and far more consistent in their judgments. 11. When researchers compared human-made sketches to AI-generated sketches under tight stroke budgets, both were similarly recognizable at higher budgets, but diverged sharply as the budget shrank. Humans and AI systems simplify drawings in fundamentally different ways once resources get scarce. 12. Reading a graph is not one single skill. It involves perception, knowing where to look, mapping that visual information onto the actual question being asked, and then translating that mapping into an answer. Each of these steps can independently break down, and people fail for very different underlying reasons even when they land on the same wrong answer. 13. When tested directly against humans on graph reading tasks, leading multimodal AI models, including GPT-4V, showed a meaningful performance gap. Even when a model's overall accuracy approached human levels, its pattern of mistakes looked nothing like how humans actually get things wrong. 14. People choose entirely different types of charts depending on what specific question they are trying to answer, not out of a generic preference for bar charts or scatter plots. Their chart choices closely tracked which visualization would genuinely help someone answer that specific question correctly. 15. Two of the most widely used graph literacy tests in education research turned out to correlate strongly with each other, suggesting they measure overlapping skills. But when researchers dug into the actual error patterns, the standard categories used in textbooks, like "find the maximum" or "identify a cluster," failed to explain why people got things wrong nearly as well as a more basic, underlying four-factor model did. 16. The deepest goal behind all of this research is not just academic curiosity. It is to eventually help students and everyday people develop genuine literacy with the visual tools that science and modern decision-making increasingly depend on, because every generation should be able to see further than the last by standing on the visual tools the previous generation built. Follow Yasmine Khosrowshahi for more ideas on thinking better, becoming clearer & building a more intentional life.

Stanford professor Judy Fan went on stage at MIT and broke down why humans are so good at making the invisible visible... And why AI hasn't actually learned to "see" the way we do. It completely changes how you think about Human Intelligence v/s Artificial Intelligence: 1. Nature never gave us straight lines or sharp corners. The number line, the coordinate plane, even basic geometry are all human inventions. We created tools that do not exist in nature simply because we needed a way to think more clearly. 2. The coordinate system Descartes invented solved a problem that had stumped mathematicians for centuries, doubling the volume of a cube. Once invented, this tool became so indispensable that virtually every math curriculum on Earth still depends on it. 3. Humans have been doing this for at least 30,000 to 80,000 years. The story of human progress is inseparable from the story of marking up our environment, from cave walls to Galileo's telescope to Feynman diagrams of particles we will never see with our own eyes. 4. Every major scientific breakthrough relied on a visual tool that made something invisible visible. Darwin needed side-by-side illustrations of finches to see variation that was otherwise too subtle to notice. Cajal needed detailed drawings of neurons under a microscope to map how the nervous system was wired. 5. Fan's research group studies something deceptively simple: how people decide what to put into a drawing and what to leave out. When two people played a drawing game, sketchers used far more detail when the target object had close competitors than when it stood alone, all the way down to using fewer strokes and less time when more detail was not necessary. 6. People are not just copying what they see. They are making constant judgment calls about what level of detail actually serves the goal of communication, and they do this naturally without ever being taught the theory behind it. 7. There is a real difference between drawing something so someone can identify it and drawing something so someone can understand how it works. In one study, participants drew explanatory diagrams that emphasized moving, causal parts of a machine while depictive drawings emphasized background and overall appearance, even though both were drawing the exact same object. 8. Explanatory drawings were genuinely better at helping someone figure out how to operate a machine, but worse at helping someone identify which machine it actually was. You cannot optimize a single drawing for both goals at once. Communication always involves tradeoffs. 9. AI vision models trained on photographs generalize surprisingly well to simple, sparse sketches, suggesting that resemblance based recognition is not just a story we tell ourselves. It is something modern neural networks can replicate with real accuracy. 10. But there remains a large, measurable gap between how confidently AI models recognize sketches and how confidently humans do, even when both groups answer the same questions about the same images. Humans are simply far more reliable and far more consistent in their judgments. 11. When researchers compared human-made sketches to AI-generated sketches under tight stroke budgets, both were similarly recognizable at higher budgets, but diverged sharply as the budget shrank. Humans and AI systems simplify drawings in fundamentally different ways once resources get scarce. 12. Reading a graph is not one single skill. It involves perception, knowing where to look, mapping that visual information onto the actual question being asked, and then translating that mapping into an answer. Each of these steps can independently break down, and people fail for very different underlying reasons even when they land on the same wrong answer. 13. When tested directly against humans on graph reading tasks, leading multimodal AI models, including GPT-4V, showed a meaningful performance gap. Even when a model's overall accuracy approached human levels, its pattern of mistakes looked nothing like how humans actually get things wrong. 14. People choose entirely different types of charts depending on what specific question they are trying to answer, not out of a generic preference for bar charts or scatter plots. Their chart choices closely tracked which visualization would genuinely help someone answer that specific question correctly. 15. Two of the most widely used graph literacy tests in education research turned out to correlate strongly with each other, suggesting they measure overlapping skills. But when researchers dug into the actual error patterns, the standard categories used in textbooks, like "find the maximum" or "identify a cluster," failed to explain why people got things wrong nearly as well as a more basic, underlying four-factor model did. 16. The deepest goal behind all of this research is not just academic curiosity. It is to eventually help students and everyday people develop genuine literacy with the visual tools that science and modern decision-making increasingly depend on, because every generation should be able to see further than the last by standing on the visual tools the previous generation built. Follow Yasmine Khosrowshahi for more ideas on thinking better, becoming clearer & building a more intentional life.

Yasmine Khosrowshahi

891,610 Aufrufe • vor 2 Monaten

⚠️Your phone scans for WiFi networks 24/7 📡 Even when you're not connected. This is what they build from those scans 🧵👇 Let me explain every single piece of this surveillance system so normies can understand what's happening to them right now. THE TARGET DEVICE PROFILE (Top Left) 📱 Device ID: DEV-7A3F9B First Seen: SUN 10:14 AM at CHURCH ⛪ That's YOU. One scan at church Sunday morning and you're permanently in their system. From that SINGLE capture, they mapped: • 36 WiFi networks you passed by 📶 • 7 locations in your daily life 📍 • Your complete daily routine 🔄 • 16 people you're regularly near 👥 All PASSIVELY. You didn't connect to any WiFi. Your phone just scanned. THE NETWORK MAP (Center) 🗺️ Each circle is a place in YOUR life identified by WiFi networks your phone detected: ⛪ CHURCH (purple): CalvaryChapel_Guest 🏠 HOME (dark blue): Smith_Family_5G 🏢 OFFICE (green): TechCorp_Internal 💪 GYM (pink): FitLife_Premium 🛒 GROCERY (green): FreshMart_WiFi ☕ COFFEE SHOP (orange): BlueMug_Public 🏫 KIDS' SCHOOL (pink): OakviewElem_Staff 🏘️ NEIGHBOR (blue): Johnson_Net_2.4G Your phone sees your neighbor's WiFi from your house → They know you live next door to that address 🏠 Your phone sees school WiFi → They know you have kids 👨‍👩‍👧‍👦 Your phone sees office WiFi 8am-5pm → They know where you work 💼 THE WIFI PROBE LOG (Bottom Left) 📊 This is the raw data your phone is SCREAMING into the void: 📡 PROBE: FitLife_Premium | -70dBm 📡 PROBE: FreshMart_WiFi | -65dBm 📡 PROBE: BlueMug_Public | -73dBm Every network. Every router. Every signal strength. They're building a TIMELINE of everywhere you go with PRECISION ⏱️ Signal strength tells them how CLOSE you are to each spot. THE AI INFERENCE ENGINE (Bottom Right) 🤖 Now AI takes that raw data and starts GUESSING about your life: 🏠 HOME: Smith_Family_5G detected every night = Your address identified 💼 WORK: TechCorp_Internal detected 8AM-5PM = Your employer identified 👨‍👩‍👧 FAMILY: OakviewElem detected = You have school-age kids ☕ ROUTINE: BlueMug_Public every morning = You're a coffee regular 🏘️ NEIGHBOR: Johnson_Net_2.4G = They mapped your neighborhood The AI doesn't just see locations 📍 It builds PATTERN RECOGNITION 🧠 You hit the gym every Monday/Wednesday at 6pm 💪 You grab coffee every weekday at 7:15am ☕ You're at church every Sunday 10am-11:30am ⛪ You shop groceries every Thursday evening 🛒 They know your routine better than your own family💀 THE PART EVERYONE MISSES ⚠️ This WiFi fingerprint thing? IT'S JUST ONE LAYER OF A SEVEN-LAYER SURVEILLANCE CAKE 🎂 📍 Geofence capture (grabbing your device ID at church/events) 📶 WiFi fingerprinting (what you're seeing here) 🔵 Bluetooth proximity logging (tracking who you're near) 📡 Cell tower triangulation (backup tracking when no WiFi) 🛰️ GPS coordinate harvesting (from apps demanding location permission) 📲 Device advertising ID (linking to your web browsing) 🕸️ Social graph mapping (connecting all your relationships) Each layer feeds the others 🔄 The geofence grabbed you at church ⛪ The WiFi mapped your entire life 🗺️ Bluetooth logged everyone you sat near 👥 Cell towers tracked you driving 🚗 GPS confirmed exact coordinates 🎯 Your ad ID linked your web history 💻 The social graph connected your whole network 🕸️ THEY BUILD A COMPLETE FILE ON YOU 📂 Who you are ✅ Where you live ✅ Where you work ✅ What you believe ✅ Who your friends are ✅ What your routines are ✅ What your weaknesses are ✅ All from PASSIVE SCANNING 📡 No warrant ❌ No consent ❌ No notification ❌ THE COMPANIES DOING THIS RIGHT NOW 🏢 This isn't conspiracy theory. Real companies selling this data TODAY: GroundTruth Selling church geofence data 📍⛪ Mobilewalla Profiling every device owner 📱👤 Placer.ai Tracking where you shop 🛒📊 Cuebiq Harvesting location pings 📡🎯 SafeGraph Selling POI visit patterns 🗺️💰 They call it "location intelligence for brands and campaigns" 🎯 Translation: They're selling your life 💰 WHAT YOU CAN DO (BUT IT'S NOT ENOUGH) 🛡️ 📱 iPhone: Settings > Privacy & Security > Location Services > System Services > Networking & Wireless > OFF 🤖 Android: Settings > Location > WiFi scanning > OFF But real talk? You're STILL vulnerable through Bluetooth and cell towers 📡 The only actual defense is leaving your phone at home 🏠 Which they KNOW you won't do 😏 WHY THIS MATTERS FOR POLITICAL TARGETING 🎯 🌍 Foreign governments BUY this data from brokers 🗳️ Political campaigns use it for micro-targeting 🎭 Influence operations identify high-value targets 📺 Propaganda gets personalized to YOUR movement patterns They know you go to church ⛪ They know your routine 🔄 They know your social circle 👥 Now they can hit you with AI-generated content designed SPECIFICALLY for someone with your exact profile 🤖 🔗THE TPUSA/SUPERFEED/AZ GOVERNMENT CONTROL/MAKE HEAVEN (HELL) CROWDED = CONNECTION 🔗 My TPUSA investigation documents Superfeed Technologies selling geofencing to churches and political orgs 📄 This WiFi fingerprinting layer is HOW they build the targeting profiles 🎯 Then they use those profiles for what they call "ministry outreach" ⛪ But it's SURVEILLANCE wrapped in religious language 🙏 Funded by FOREIGN MONEY💰 BOTTOM LINE ⚡ 📱 Your phone is a 24/7 surveillance device 📶 WiFi fingerprint is just ONE targeting layer 🏢 Commercial companies sell your complete life pattern 🌍 Foreign governments buy it 🎯 Political operations weaponize it And 99% of Americans have NO IDEA it's happening 💀 Share this if you think people should know they're being tracked 🔁💥

Danks

94,617 Aufrufe • vor 6 Monaten

A new father became so terrified of never learning anything again that he accidentally dismantled the biggest lie in education. His name is Josh Kaufman, and he wasn't a neuroscientist or a professor. He was an author working from home, running a business with his wife, with a newborn daughter who had just obliterated any concept of free time he thought he had. Around week 8 of sleep deprivation, he had the thought every parent has. I am never going to learn anything new ever again. And because he was the kind of person who responds to panic with research, he went to the library and started reading everything he could find about how humans acquire skills. He read book after book, study after study. Every single one said the same thing. 10,000 hours. He had a full-body reaction to that number. 10,000 hours is a full-time job for five years. He didn't have five years. He didn't have five hours. He had a newborn and a business and a wife who was also building a business in the same house. So he kept digging. And here is where it gets interesting. The 10,000 hour rule came from a researcher named K. Anders Ericsson at Florida State University. What Ericsson actually studied was professional athletes, world-class musicians, chess grandmasters people at the absolute tip of ultra-competitive, ultra-high-performing fields. His finding was that the people at the very top of those narrow fields had put in around 10,000 hours of deliberate practice. That is all the finding said. Then Malcolm Gladwell wrote Outliers in 2007, and the message went through a game of telephone that destroyed its meaning entirely. It takes 10,000 hours to reach the top of an ultra-competitive field became it takes 10,000 hours to become an expert, which became it takes 10,000 hours to become good at something, which became it takes 10,000 hours to learn something. That last statement is completely false. And the actual research had been showing something different the entire time. When cognitive psychologists study skill acquisition, they measure a graph that looks identical across every domain they have ever tested. At the start, performance is terrible. With a small amount of practice, it improves rapidly. Then it plateaus, and subsequent gains become much harder and slower to achieve. The steep part of that curve the jump from knowing nothing to being reasonably good happens much faster than anyone tells you. Not 10,000 hours. Not 1,000 hours. 20 hours. Kaufman tested this himself. He had always wanted to learn ukulele. He picked one up, put 20 hours of focused deliberate practice into it, and stood on a TEDx stage playing a medley of recognizable pop songs in front of a live audience. The crowd went wild. He then told them that performance was his 20th hour. But 20 hours is not just a number. There is a method inside it. The first step is to deconstruct the skill. Most things we think of as single skills are actually bundles of dozens of smaller skills. You do not need all of them. You need the ones that get you to your specific goal the fastest. In music, this means most songs use four or five chords. Learn those first. Ignore the rest until they matter. The second step is to learn just enough to self-correct. Get three to five resources books, courses, videos but do not use them as a reason to delay practice. The point of learning is not to master theory first. It is to get good enough at noticing your own mistakes that you can adjust as you go. The third step is to remove barriers to practice. Not through willpower. Through structure. If the instrument is in the case in the closet, you will not play it. If your phone is in the room, you will not focus. Kaufman was brutal about this. The environment does the work that discipline cannot sustain. The fourth step is the one that actually makes the system work. Pre-commit to 20 hours before you start. Here is why this matters. Every skill has what he called a frustration barrier. The early part of learning anything is genuinely terrible. You are incompetent and you know it. That feeling is so uncomfortable that most people quit before they ever cross to the other side of the curve. By pre-committing to 20 hours, you are making a contract with yourself to push through the frustration long enough to arrive at the part where things start clicking. The barrier to learning something new is never intellectual. It is emotional. We are afraid of feeling stupid. That fear costs most people everything they could have learned. Kaufman figured this out while holding a baby and running out of time, which is the most human possible condition for having a breakthrough. Most people are waiting for the perfect season to start. He just started. 20 hours is 45 minutes a day for a month. That is it. That is the price of going from knowing nothing to being genuinely capable at almost anything you can name. The 10,000 hour rule was never about learning. It was about becoming the best in the world. You probably do not need to be the best in the world. You just need to start.

A new father became so terrified of never learning anything again that he accidentally dismantled the biggest lie in education. His name is Josh Kaufman, and he wasn't a neuroscientist or a professor. He was an author working from home, running a business with his wife, with a newborn daughter who had just obliterated any concept of free time he thought he had. Around week 8 of sleep deprivation, he had the thought every parent has. I am never going to learn anything new ever again. And because he was the kind of person who responds to panic with research, he went to the library and started reading everything he could find about how humans acquire skills. He read book after book, study after study. Every single one said the same thing. 10,000 hours. He had a full-body reaction to that number. 10,000 hours is a full-time job for five years. He didn't have five years. He didn't have five hours. He had a newborn and a business and a wife who was also building a business in the same house. So he kept digging. And here is where it gets interesting. The 10,000 hour rule came from a researcher named K. Anders Ericsson at Florida State University. What Ericsson actually studied was professional athletes, world-class musicians, chess grandmasters people at the absolute tip of ultra-competitive, ultra-high-performing fields. His finding was that the people at the very top of those narrow fields had put in around 10,000 hours of deliberate practice. That is all the finding said. Then Malcolm Gladwell wrote Outliers in 2007, and the message went through a game of telephone that destroyed its meaning entirely. It takes 10,000 hours to reach the top of an ultra-competitive field became it takes 10,000 hours to become an expert, which became it takes 10,000 hours to become good at something, which became it takes 10,000 hours to learn something. That last statement is completely false. And the actual research had been showing something different the entire time. When cognitive psychologists study skill acquisition, they measure a graph that looks identical across every domain they have ever tested. At the start, performance is terrible. With a small amount of practice, it improves rapidly. Then it plateaus, and subsequent gains become much harder and slower to achieve. The steep part of that curve the jump from knowing nothing to being reasonably good happens much faster than anyone tells you. Not 10,000 hours. Not 1,000 hours. 20 hours. Kaufman tested this himself. He had always wanted to learn ukulele. He picked one up, put 20 hours of focused deliberate practice into it, and stood on a TEDx stage playing a medley of recognizable pop songs in front of a live audience. The crowd went wild. He then told them that performance was his 20th hour. But 20 hours is not just a number. There is a method inside it. The first step is to deconstruct the skill. Most things we think of as single skills are actually bundles of dozens of smaller skills. You do not need all of them. You need the ones that get you to your specific goal the fastest. In music, this means most songs use four or five chords. Learn those first. Ignore the rest until they matter. The second step is to learn just enough to self-correct. Get three to five resources books, courses, videos but do not use them as a reason to delay practice. The point of learning is not to master theory first. It is to get good enough at noticing your own mistakes that you can adjust as you go. The third step is to remove barriers to practice. Not through willpower. Through structure. If the instrument is in the case in the closet, you will not play it. If your phone is in the room, you will not focus. Kaufman was brutal about this. The environment does the work that discipline cannot sustain. The fourth step is the one that actually makes the system work. Pre-commit to 20 hours before you start. Here is why this matters. Every skill has what he called a frustration barrier. The early part of learning anything is genuinely terrible. You are incompetent and you know it. That feeling is so uncomfortable that most people quit before they ever cross to the other side of the curve. By pre-committing to 20 hours, you are making a contract with yourself to push through the frustration long enough to arrive at the part where things start clicking. The barrier to learning something new is never intellectual. It is emotional. We are afraid of feeling stupid. That fear costs most people everything they could have learned. Kaufman figured this out while holding a baby and running out of time, which is the most human possible condition for having a breakthrough. Most people are waiting for the perfect season to start. He just started. 20 hours is 45 minutes a day for a month. That is it. That is the price of going from knowing nothing to being genuinely capable at almost anything you can name. The 10,000 hour rule was never about learning. It was about becoming the best in the world. You probably do not need to be the best in the world. You just need to start.

Ihtesham Ali

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