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For 300 years mathematicians solved polynomials of degree 1, 2, 3, and 4 with increasingly complex formulas. Then they hit degree 5 and the formula simply doesn't exist - not undiscovered, provably impossible. The reason is group theory. The 5 solutions of a quintic can be scrambled in ways... show more

Eron

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This is actually insane and whoever promised him this….smh Let’s address some stupid things fans are saying: 1. Burrow wouldn’t have won the natty with that 2023 defense either 2. 5 shouldn’t have been promised without speaking to JD5 since you promised him the number wouldn’t be worn 3. Florida and Oklahoma have statues of Baker, Tebow, and all their Heisman winners so not the same thing. 4. 5 is way more apart of JD5’s NIL than 9 was for Burrow, we literally call him 5 5. JD5 is the reason the program is not in a dark place—can you imagine not having 2022 & 2023 and instead of just the past 2 years being the worst in my lifetime, having that for 4 straight years???

This is actually insane and whoever promised him this….smh Let’s address some stupid things fans are saying: 1. Burrow wouldn’t have won the natty with that 2023 defense either 2. 5 shouldn’t have been promised without speaking to JD5 since you promised him the number wouldn’t be worn 3. Florida and Oklahoma have statues of Baker, Tebow, and all their Heisman winners so not the same thing. 4. 5 is way more apart of JD5’s NIL than 9 was for Burrow, we literally call him 5 5. JD5 is the reason the program is not in a dark place—can you imagine not having 2022 & 2023 and instead of just the past 2 years being the worst in my lifetime, having that for 4 straight years???

LChris

28,713 Aufrufe • vor 1 Monat

The area under the bell curve has no formula. Mathematicians proved that in 1830 — not that nobody found it yet, that it literally cannot exist. Then someone squared the integral, switched to polar coordinates, and got √π in four minutes. The same curve LLMs assume for weight noise and gradient errors. The trick: squaring turns one line integral into a surface over a plane. Suddenly x²+y² appears in the exponent — that's a circle, hiding inside e^(-x²) the whole time. Polar coordinates hand you a free factor of r, the chain rule clicks, and the "impossible" integral collapses to π. Every GPU training run assumes this result thousands of times per second. 14 minutes. Bookmark & watch today.

The area under the bell curve has no formula. Mathematicians proved that in 1830 — not that nobody found it yet, that it literally cannot exist. Then someone squared the integral, switched to polar coordinates, and got √π in four minutes. The same curve LLMs assume for weight noise and gradient errors. The trick: squaring turns one line integral into a surface over a plane. Suddenly x²+y² appears in the exponent — that's a circle, hiding inside e^(-x²) the whole time. Polar coordinates hand you a free factor of r, the chain rule clicks, and the "impossible" integral collapses to π. Every GPU training run assumes this result thousands of times per second. 14 minutes. Bookmark & watch today.

Deliriumm

31,467 Aufrufe • vor 11 Tagen

Many people hear of the scribal differences in documents like the biblical books and they think that’s a problem. The irony is that the more copies that we have (even with all the mistakes), the higher degree of confidence we can know that we have the original because of the field and discipline of Textual Criticism.

Many people hear of the scribal differences in documents like the biblical books and they think that’s a problem. The irony is that the more copies that we have (even with all the mistakes), the higher degree of confidence we can know that we have the original because of the field and discipline of Textual Criticism.

Wes Huff

93,854 Aufrufe • vor 10 Monaten

EXTREMELY CONCERNING 🚨 Today: Moms Across America just got back their toxic metals testing results for baby formula They tested 20 brands including organic, “All of them, a 100% of the 40 samples tested positive for toxic aluminum and lead. All of them. 80% of the samples had lead levels that were higher than what the EPA allows in drinking water. This is very disturbing. Lead is super toxic and harmful for brain development. At 41,000 parts per billion of aluminum in one of the goat's milk baby formulas, that level was 4,000 to 40,000 times higher than the other heavy metals that were found in the, in baby formulas. And that level, when consumed on a daily basis at a normal rate, the way babies normally do, will exceed what the FDA allows in drinking water, or for consumption for of aluminum for a preemie baby. So these babies are getting toxic levels of aluminum in this goat's milk baby formula. It's called, Cabrida. The highest aluminum levels detected was 200 times higher than what the EPA allows in drinking water. That's in that goat's milk formula. The 57% of the samples tested positive for arsenic, 55% for mercury, and 35% for cadmium. Levels of mercury in 4 of the samples were detected above the amounts allowed by the FDA in drinking water, that's 10%. And levels of cadmium in, both samples of one formula were nearly twice the level allowed in drinking water. So the cadmium can cause cancer. Mercury is very toxic as well, can cause all kinds of sicknesses. 6 of the 20 formulas were positive for all 5 toxic metals in both samples.” “We had hoped at least some of them, perhaps maybe the organic ones or the goat milk formulas, would not have toxic heavy metals, but we were wrong.” HOW DOES THIS HAPPEN??

EXTREMELY CONCERNING 🚨 Today: Moms Across America just got back their toxic metals testing results for baby formula They tested 20 brands including organic, “All of them, a 100% of the 40 samples tested positive for toxic aluminum and lead. All of them. 80% of the samples had lead levels that were higher than what the EPA allows in drinking water. This is very disturbing. Lead is super toxic and harmful for brain development. At 41,000 parts per billion of aluminum in one of the goat's milk baby formulas, that level was 4,000 to 40,000 times higher than the other heavy metals that were found in the, in baby formulas. And that level, when consumed on a daily basis at a normal rate, the way babies normally do, will exceed what the FDA allows in drinking water, or for consumption for of aluminum for a preemie baby. So these babies are getting toxic levels of aluminum in this goat's milk baby formula. It's called, Cabrida. The highest aluminum levels detected was 200 times higher than what the EPA allows in drinking water. That's in that goat's milk formula. The 57% of the samples tested positive for arsenic, 55% for mercury, and 35% for cadmium. Levels of mercury in 4 of the samples were detected above the amounts allowed by the FDA in drinking water, that's 10%. And levels of cadmium in, both samples of one formula were nearly twice the level allowed in drinking water. So the cadmium can cause cancer. Mercury is very toxic as well, can cause all kinds of sicknesses. 6 of the 20 formulas were positive for all 5 toxic metals in both samples.” “We had hoped at least some of them, perhaps maybe the organic ones or the goat milk formulas, would not have toxic heavy metals, but we were wrong.” HOW DOES THIS HAPPEN??

Wall Street Apes

662,172 Aufrufe • vor 2 Jahren

I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.

I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.

Bartosz Naskręcki

44,467 Aufrufe • vor 4 Monaten

.Secretary Marco Rubio praises the early success of the Board of Peace on Gaza: "We hope that this can serve as a model for other complex and difficult situations, so they can be solved in the same way."

.Secretary Marco Rubio praises the early success of the Board of Peace on Gaza: "We hope that this can serve as a model for other complex and difficult situations, so they can be solved in the same way."

Rapid Response 47

28,421 Aufrufe • vor 7 Monaten

Andrew Ng and AMD CEO revealed the plan How anyone can become a $40k AI engineer from scratch: 00:00 - one engineer with AI can replace 5 employees 14:15 - one day with AI can replace 3 months of work 23:28 - how to build a profitable company for $20 This free 26-minute talk is worth more than a $90,000 Stanford AI degree Bookmark and watch it today Then read the article below

Andrew Ng and AMD CEO revealed the plan How anyone can become a $40k AI engineer from scratch: 00:00 - one engineer with AI can replace 5 employees 14:15 - one day with AI can replace 3 months of work 23:28 - how to build a profitable company for $20 This free 26-minute talk is worth more than a $90,000 Stanford AI degree Bookmark and watch it today Then read the article below

rari

57,158 Aufrufe • vor 2 Monaten

Vitalik Buterin explains why proof-of-stake is more secure than proof-of-work “I think proof of stake is very secure because to attack the system, you need to have basically as much stake as the rest of the network. Right now, for example, we have 5 million ETH staking, which means you have to come up with 5 million ETH and then join the network.” At the time of this writing, more than 37 million ETH are being staked, with 3 million ETH waiting to join via the validator queue. At today’s prices, that’s more than $80 billion of ETH someone would have to acquire to attack the network and revert finalized blocks, which is more than the cost of attacking even the Bitcoin network by some estimates. The other defense mechanism that proof-of-stake has that proof-of-work doesn’t is slashing, which makes Ethereum antifragile. Vitalik explains: “Recovering from attacks is much easier in proof-of-stake than proof-of-work. For many kinds of attacks you do against [the Ethereum] network, we have this concept of automatic slashing. In order to revert a finalized block, you basically have to have a big portion of your validators sign two conflicting messages. This is something where once these messages are on the network, you can go and prove ‘these people did it.’ So we have this feature in the protocol where you basically take all these people who provably misbehaved and you burn their coins.” Vitalik also acknowledges the possibility of censoring attacks, where if 1/3rd of validators refuse to attest, the chain can’t finalize. But, as he explains, Ethereum has a contingency plan for this as well: “Everyone who got censored would create a minority chain, and the community would have to do a soft fork. The would have to say, ‘this chain is clearly attacking us and this one is not attacking us, so we’re going to join this chain.’ Then what happens is, on that new chain, the attackers also lose a lot of coins. The difference between proof-of-stake and proof-of-work is that in a proof-of-stake system, you can identify specific participants — and this isn’t a human going in and saying ‘I don’t like you’. It’s all automated.” One last benefit of proof-of-stake is that security scales with the value of the network. As Vitalik put it five years ago, it is really relative security, and not absolute security, that matters: “The security needs of a thing have to be proportional to the size of that thing, because as a thing gets bigger, its enemies become bigger and more well-motivated. If BTC were 100x as big as it is today, the value from destroying it would be 100x higher, and the kinds of actors that would want to care about destroying it would be much bigger and scarier. This is also why countries of all sizes have roughly similarly sized militaries as a percentage of GDP. Hence, cost of attack divided by market cap really is the correct statistic to measure, and in the long run issuance-free PoW really does look not that good." Source: Lex Fridman (Jun 2021)

Vitalik Buterin explains why proof-of-stake is more secure than proof-of-work “I think proof of stake is very secure because to attack the system, you need to have basically as much stake as the rest of the network. Right now, for example, we have 5 million ETH staking, which means you have to come up with 5 million ETH and then join the network.” At the time of this writing, more than 37 million ETH are being staked, with 3 million ETH waiting to join via the validator queue. At today’s prices, that’s more than $80 billion of ETH someone would have to acquire to attack the network and revert finalized blocks, which is more than the cost of attacking even the Bitcoin network by some estimates. The other defense mechanism that proof-of-stake has that proof-of-work doesn’t is slashing, which makes Ethereum antifragile. Vitalik explains: “Recovering from attacks is much easier in proof-of-stake than proof-of-work. For many kinds of attacks you do against [the Ethereum] network, we have this concept of automatic slashing. In order to revert a finalized block, you basically have to have a big portion of your validators sign two conflicting messages. This is something where once these messages are on the network, you can go and prove ‘these people did it.’ So we have this feature in the protocol where you basically take all these people who provably misbehaved and you burn their coins.” Vitalik also acknowledges the possibility of censoring attacks, where if 1/3rd of validators refuse to attest, the chain can’t finalize. But, as he explains, Ethereum has a contingency plan for this as well: “Everyone who got censored would create a minority chain, and the community would have to do a soft fork. The would have to say, ‘this chain is clearly attacking us and this one is not attacking us, so we’re going to join this chain.’ Then what happens is, on that new chain, the attackers also lose a lot of coins. The difference between proof-of-stake and proof-of-work is that in a proof-of-stake system, you can identify specific participants — and this isn’t a human going in and saying ‘I don’t like you’. It’s all automated.” One last benefit of proof-of-stake is that security scales with the value of the network. As Vitalik put it five years ago, it is really relative security, and not absolute security, that matters: “The security needs of a thing have to be proportional to the size of that thing, because as a thing gets bigger, its enemies become bigger and more well-motivated. If BTC were 100x as big as it is today, the value from destroying it would be 100x higher, and the kinds of actors that would want to care about destroying it would be much bigger and scarier. This is also why countries of all sizes have roughly similarly sized militaries as a percentage of GDP. Hence, cost of attack divided by market cap really is the correct statistic to measure, and in the long run issuance-free PoW really does look not that good." Source: Lex Fridman (Jun 2021)

Etherealize

102,150 Aufrufe • vor 6 Monaten

First, Happy New Year everyone! It's been a wild ride. I can't wait for 2026, LFG! I love you all! ❤️ Second, here's my conversation with Joel David Hamkins (Joel David Hamkins), mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity. We talk about paradoxes that challenged some of the greatest mathematicians of the 20th century, Gödel Incompleteness theorems, the mathematical multiverse, the nature of truth, computation, and much more. By the way, Joel is the #1 highest-rated user on MathOverflow, and writes a great blog called "Infinitely More". It's here on X in full and is up everywhere else (see comment). Timestamps: 0:00 - Introduction 2:17 - Infinity & paradoxes 49:27 - Russell's paradox 1:02:35 - Gödel's incompleteness theorems 1:20:06 - Truth vs proof 1:31:30 - The Halting Problem 1:47:23 - Does infinity exist? 2:04:57 - MathOverflow 2:08:49 - The Continuum Hypothesis 2:18:36 - Hardest problems in mathematics 2:28:03 - Mathematical multiverse 2:46:55 - Surreal numbers 2:57:33 - Conway's Game of Life 2:59:49 - Computability theory 3:09:41 - P vs NP 3:12:58 - Greatest mathematicians in history 3:26:43 - Infinite chess 3:45:01 - Most beautiful idea in mathematics

First, Happy New Year everyone! It's been a wild ride. I can't wait for 2026, LFG! I love you all! ❤️ Second, here's my conversation with Joel David Hamkins (Joel David Hamkins), mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity. We talk about paradoxes that challenged some of the greatest mathematicians of the 20th century, Gödel Incompleteness theorems, the mathematical multiverse, the nature of truth, computation, and much more. By the way, Joel is the #1 highest-rated user on MathOverflow, and writes a great blog called "Infinitely More". It's here on X in full and is up everywhere else (see comment). Timestamps: 0:00 - Introduction 2:17 - Infinity & paradoxes 49:27 - Russell's paradox 1:02:35 - Gödel's incompleteness theorems 1:20:06 - Truth vs proof 1:31:30 - The Halting Problem 1:47:23 - Does infinity exist? 2:04:57 - MathOverflow 2:08:49 - The Continuum Hypothesis 2:18:36 - Hardest problems in mathematics 2:28:03 - Mathematical multiverse 2:46:55 - Surreal numbers 2:57:33 - Conway's Game of Life 2:59:49 - Computability theory 3:09:41 - P vs NP 3:12:58 - Greatest mathematicians in history 3:26:43 - Infinite chess 3:45:01 - Most beautiful idea in mathematics

Lex Fridman

517,621 Aufrufe • vor 9 Monaten

The first 10 trillion non-trivial zeros of the Riemann zeta function all sit exactly on the line where the real part equals 1/2. Every single one. And yet after 165 years nobody can prove it must be true - the Clay Institute offers $1 million for a proof. The prime numbers hidden inside these zeros are what make RSA encryption unbreakable - the same math that protects every LLM API key, bank transfer, and password on the internet. 38 minutes. Bookmark & watch today. The most beautiful unsolved problem in mathematics.

The first 10 trillion non-trivial zeros of the Riemann zeta function all sit exactly on the line where the real part equals 1/2. Every single one. And yet after 165 years nobody can prove it must be true - the Clay Institute offers $1 million for a proof. The prime numbers hidden inside these zeros are what make RSA encryption unbreakable - the same math that protects every LLM API key, bank transfer, and password on the internet. 38 minutes. Bookmark & watch today. The most beautiful unsolved problem in mathematics.

Eron

33,509 Aufrufe • vor 1 Monat

The dream of every Muslim is simply to be treated the same as any other New Yorker. And yet, for too long, we have been told to ask for less than that, and endure hatred and bigotry in the shadows. No more.

The dream of every Muslim is simply to be treated the same as any other New Yorker. And yet, for too long, we have been told to ask for less than that, and endure hatred and bigotry in the shadows. No more.

Zohran Kwame Mamdani

25,468,649 Aufrufe • vor 11 Monaten

"They have bought in and been okay with the hard and now the hard is not hard. I hope that will carry over for the rest of the season and the rest of their lives- that they can handle hard things. If that's what becomes of them, then it will be a good coaching job by all of us."

"They have bought in and been okay with the hard and now the hard is not hard. I hope that will carry over for the rest of the season and the rest of their lives- that they can handle hard things. If that's what becomes of them, then it will be a good coaching job by all of us."

The Winning Difference

24,377 Aufrufe • vor 7 Monaten

🚨🇺🇸 OBAMA: AMERICA IS MORE DIVIDED THAN ANY TIME IN MY LIFETIME Obama delivered a stark assessment of American democracy during his speech at Crystal Bridges Museum, claiming the country is more unstable than at any point in his lifetime and warning about the politicization of institutions: "We are more divided and our democracy is more unstable than any time in my lifetime. I would not have expected the legitimacy of an election and the peaceful transfer of power to have been challenged. I thought that was not something that would happen today. I would not expect the politicization of the Justice Department or our military. The degree to which that has been encouraged, that used to be something that I would lecture other countries not to do. You don't have your military involved in partisan politics. Its loyalty is to the Constitution. Its loyalty is not to any party. And it is not to any president." This coming from the president whose FBI leadership was texting about "insurance policies" against Trump and whose party spent four years calling the 2016 election illegitimate is pretty rich... Source: CBS 5 News

🚨🇺🇸 OBAMA: AMERICA IS MORE DIVIDED THAN ANY TIME IN MY LIFETIME Obama delivered a stark assessment of American democracy during his speech at Crystal Bridges Museum, claiming the country is more unstable than at any point in his lifetime and warning about the politicization of institutions: "We are more divided and our democracy is more unstable than any time in my lifetime. I would not have expected the legitimacy of an election and the peaceful transfer of power to have been challenged. I thought that was not something that would happen today. I would not expect the politicization of the Justice Department or our military. The degree to which that has been encouraged, that used to be something that I would lecture other countries not to do. You don't have your military involved in partisan politics. Its loyalty is to the Constitution. Its loyalty is not to any party. And it is not to any president." This coming from the president whose FBI leadership was texting about "insurance policies" against Trump and whose party spent four years calling the 2016 election illegitimate is pretty rich... Source: CBS 5 News

Mario Nawfal

82,091 Aufrufe • vor 10 Monaten

UN Secretary-General Guterres on Africa: Africa is a double victim of colonialism. First, because of colonialism itself and what colonialism has caused. We can talk about the transatlantic slave trade and many other aspects in which the African continent has been sacrificed. And then second reason why it’s a victim, because when the institutions that are today the multilateral institutions of global governance were created, the African countries, most of them, were still under colonial domination. So they were not present and they were not taken into account, and so Africa is not effectively represented in the multilateral institutions that exist today. And that is something that is a scandal that needs to be corrected.

UN Secretary-General Guterres on Africa: Africa is a double victim of colonialism. First, because of colonialism itself and what colonialism has caused. We can talk about the transatlantic slave trade and many other aspects in which the African continent has been sacrificed. And then second reason why it’s a victim, because when the institutions that are today the multilateral institutions of global governance were created, the African countries, most of them, were still under colonial domination. So they were not present and they were not taken into account, and so Africa is not effectively represented in the multilateral institutions that exist today. And that is something that is a scandal that needs to be corrected.

Clash Report

15,368 Aufrufe • vor 6 Tagen

Demoralisation propaganda in Australia. Entire ABC studio audience jeers Australian MP because he says he’s happy that Australia exists as a country. Then the audience cheer and clap a separatist speaker who says she is not Australian and never wants to be. This is extremely sad. It shows that many people on the far-left actually hate Australia and the concept of Australia as a unified nation state. The debate can be framed in the context of “colonisation” but the reality is that if the British had not come to Australia, the country we live in today with all the democratic freedoms we enjoy would not exist and most of us would not be living here. So when they say that it should never have happened they are saying that Australia should not exist.

Demoralisation propaganda in Australia. Entire ABC studio audience jeers Australian MP because he says he’s happy that Australia exists as a country. Then the audience cheer and clap a separatist speaker who says she is not Australian and never wants to be. This is extremely sad. It shows that many people on the far-left actually hate Australia and the concept of Australia as a unified nation state. The debate can be framed in the context of “colonisation” but the reality is that if the British had not come to Australia, the country we live in today with all the democratic freedoms we enjoy would not exist and most of us would not be living here. So when they say that it should never have happened they are saying that Australia should not exist.

Drew Pavlou 🇦🇺🇺🇸🇺🇦🇹🇼

152,386 Aufrufe • vor 1 Jahr

“The average person lives a life of luxury that previous generations could never imagine, but because of that we dont actually taste this deeper joy that I think God intends for us.” Most people today live with a level of comfort that would have looked unbelievable to almost anyone in history. Food is always available, entertainment never stops, boredom can be eliminated instantly, and almost every inconvenience can be solved with a screen and a few clicks. That’s why so many people today have everything they thought they wanted and still feel empty afterward. The strange paradox of modern life is that we have removed many of the hardships that once burdened humanity, but in the process we also removed many of the conditions that produced gratitude, resilience, depth, and dependence on God. A civilization drowning in comfort often becomes spiritually numb without even realizing it. Which is probably why some of the holiest people in history voluntarily embraced hardship even when they did not have to. They understood something we are slowly forgetting: Comfort and happiness are not the same thing.

“The average person lives a life of luxury that previous generations could never imagine, but because of that we dont actually taste this deeper joy that I think God intends for us.” Most people today live with a level of comfort that would have looked unbelievable to almost anyone in history. Food is always available, entertainment never stops, boredom can be eliminated instantly, and almost every inconvenience can be solved with a screen and a few clicks. That’s why so many people today have everything they thought they wanted and still feel empty afterward. The strange paradox of modern life is that we have removed many of the hardships that once burdened humanity, but in the process we also removed many of the conditions that produced gratitude, resilience, depth, and dependence on God. A civilization drowning in comfort often becomes spiritually numb without even realizing it. Which is probably why some of the holiest people in history voluntarily embraced hardship even when they did not have to. They understood something we are slowly forgetting: Comfort and happiness are not the same thing.

Athenaeum Book Club

64,373 Aufrufe • vor 4 Monaten

3 key takeaways from Sergey Nazarov’s conversation with Tyler Williams, Counselor to the Secretary of Treasury for Digital Assets: 1. Governments must embrace the blockchain opportunity Nations can establish global leadership in digital assets by helping their financial systems become the “highest-quality provider of assets with the most reliable infrastructure and guarantees.” 2. Automated compliance is the future “The world that you want to end up in ... is where all compliance can be completely automated.” 3. Proof of reserves is just the beginning “Proof of reserves is the beginning of a category of proof of things ... proof of liability, proof of solvency, proof of composition, proof of many things.” Watch the full discussion to understand how the Chainlink standard for cross-chain interoperability and verifiable data will transform global finance:

3 key takeaways from Sergey Nazarov’s conversation with Tyler Williams, Counselor to the Secretary of Treasury for Digital Assets: 1. Governments must embrace the blockchain opportunity Nations can establish global leadership in digital assets by helping their financial systems become the “highest-quality provider of assets with the most reliable infrastructure and guarantees.” 2. Automated compliance is the future “The world that you want to end up in ... is where all compliance can be completely automated.” 3. Proof of reserves is just the beginning “Proof of reserves is the beginning of a category of proof of things ... proof of liability, proof of solvency, proof of composition, proof of many things.” Watch the full discussion to understand how the Chainlink standard for cross-chain interoperability and verifiable data will transform global finance:

Chainlink

41,329 Aufrufe • vor 1 Jahr