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The Man Who Revolutionized Computer Science With Math

The Man Who Revolutionized Computer Science With Math

Read the full transcript of "The Man Who Revolutionized Computer Science With Math" by Quanta Magazine. Practice English listening and reading with interacti...

Channel: Quanta Magazine Duration: 7 min Sentences: 60
Leslie Lamport revolutionized how computers talk to each other. The Turing Award-winning computer scientist pioneered the field of distributed systems, where multiple components on different networks coordinate to achieve a common objective. (Internet searches, cloud computing and artificial intelligence all involve orchestrating legions of powerful computing machines to work together.) In the early 1980s, Lamport also created LaTeX, a document preparation system that provides sophisticated ways to typeset complex formulas and format scientific documents. In 1989, Lamport invented Paxos, a “consensus algorithm” that allows multiple computers to execute complex tasks; without it, modern computing could not exist. He’s also brought more attention to a handful of problems, giving them distinctive names like the bakery algorithm and the Byzantine Generals Problem. Lamport’s work since the 1990s has focused on “formal verification,” the use of mathematical proofs to verify the correctness of software and hardware systems. Notably, he created a “specification language” called TLA+ (for Temporal Logic of Actions), which employs the precise language of mathematics to prevent bugs and avoid design flaws. Read more at Quanta Magazine: https://www.quantamagazine.org/bringing-mathematical-perfection-to-software-20220516/ - VISIT our Website: https://www.quantamagazine.org - LIKE us on Facebook: https://www.facebook.com/QuantaNews - FOLLOW us Twitter: https://twitter.com/QuantaMagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation https://www.simonsfoundation.org/ #computerscience #math
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7.0s my name is lesie Lamport and I am a my name is lesie Lamport and I am a computer computer computer scientist uh which is something that scientist uh which is something that scientist uh which is something that didn't really exist when I started being didn't really exist when I started being
7.0s my name is lesie Lamport and I am a computer
8.2s computer
8.2s computer scientist uh which is something that
10.9s scientist uh which is something that
11.0s scientist uh which is something that didn't really exist when I started being
13.4s didn't really exist when I started being
13.4s didn't really exist when I started being a computer scientist and it took me a a computer scientist and it took me a a computer scientist and it took me a while to figure out that I was one my while to figure out that I was one my
15.6s a computer scientist and it took me a
15.6s a computer scientist and it took me a while to figure out that I was one my
18.5s while to figure out that I was one my
18.5s while to figure out that I was one my relationship with computers began as a relationship with computers began as a relationship with computers began as a programmer it never quite occurred to me programmer it never quite occurred to me programmer it never quite occurred to me that I was doing anything scientific that I was doing anything scientific
21.4s relationship with computers began as a
21.4s relationship with computers began as a programmer it never quite occurred to me
23.8s programmer it never quite occurred to me
23.8s programmer it never quite occurred to me that I was doing anything scientific
26.3s that I was doing anything scientific
26.3s that I was doing anything scientific until after I had published enough until after I had published enough until after I had published enough papers that if finally occurred to me my papers that if finally occurred to me my papers that if finally occurred to me my education was as a mathematician it was
28.5s until after I had published enough
28.5s until after I had published enough papers that if finally occurred to me my
32.1s papers that if finally occurred to me my
32.1s papers that if finally occurred to me my education was as a mathematician it was
34.4s education was as a mathematician it was education was as a mathematician it was just natural for me to think about just natural for me to think about just natural for me to think about computers as a computers as a computers as a mathematician when you write an mathematician when you write an
34.4s education was as a mathematician it was just natural for me to think about
37.3s just natural for me to think about
37.3s just natural for me to think about computers as a
39.0s computers as a
39.0s computers as a mathematician when you write an
41.1s mathematician when you write an
41.2s mathematician when you write an algorithm you need to have a proof that algorithm you need to have a proof that algorithm you need to have a proof that it's correct an algorithm without a it's correct an algorithm without a it's correct an algorithm without a proof is a conjecture it's not a
44.1s algorithm you need to have a proof that
44.1s algorithm you need to have a proof that it's correct an algorithm without a
46.5s it's correct an algorithm without a
46.6s it's correct an algorithm without a proof is a conjecture it's not a
50.4s proof is a conjecture it's not a proof is a conjecture it's not a theorem and if you're proving things theorem and if you're proving things theorem and if you're proving things well that means well that means well that means mathematics computer scientists tend to mathematics computer scientists tend to
50.4s proof is a conjecture it's not a theorem and if you're proving things
53.8s theorem and if you're proving things
53.8s theorem and if you're proving things well that means
55.7s well that means
55.7s well that means mathematics computer scientists tend to
58.5s mathematics computer scientists tend to
58.6s mathematics computer scientists tend to think in terms of programming languages think in terms of programming languages think in terms of programming languages one of the epiphanies in my career was one of the epiphanies in my career was one of the epiphanies in my career was the realization that I was not writing
61.2s think in terms of programming languages
61.2s think in terms of programming languages one of the epiphanies in my career was
64.5s one of the epiphanies in my career was
64.5s one of the epiphanies in my career was the realization that I was not writing
67.0s the realization that I was not writing the realization that I was not writing programs as a computer scientist I was programs as a computer scientist I was programs as a computer scientist I was designing algorithms I came to realize designing algorithms I came to realize
67.0s the realization that I was not writing programs as a computer scientist I was
69.4s programs as a computer scientist I was
69.4s programs as a computer scientist I was designing algorithms I came to realize
72.3s designing algorithms I came to realize
72.3s designing algorithms I came to realize that if I'm not writing a program I that if I'm not writing a program I that if I'm not writing a program I shouldn't use a programming shouldn't use a programming shouldn't use a programming language people confuse programming with language people confuse programming with
74.7s that if I'm not writing a program I
74.7s that if I'm not writing a program I shouldn't use a programming
76.7s shouldn't use a programming
76.7s shouldn't use a programming language people confuse programming with
80.0s language people confuse programming with
80.0s language people confuse programming with coding coding is to programming what coding coding is to programming what coding coding is to programming what typing is to writing writing is typing is to writing writing is typing is to writing writing is something that involves mental effort something that involves mental effort
83.3s coding coding is to programming what
83.4s coding coding is to programming what typing is to writing writing is
85.6s typing is to writing writing is
85.6s typing is to writing writing is something that involves mental effort
87.6s something that involves mental effort
87.6s something that involves mental effort you're thinking about what you're going you're thinking about what you're going you're thinking about what you're going to say the words have some importance to say the words have some importance to say the words have some importance but in some sense that even they are but in some sense that even they are
89.1s you're thinking about what you're going
89.1s you're thinking about what you're going to say the words have some importance
91.4s to say the words have some importance
91.4s to say the words have some importance but in some sense that even they are
93.4s but in some sense that even they are
93.4s but in some sense that even they are secondary to the ideas in the same way secondary to the ideas in the same way secondary to the ideas in the same way programs are built on ideas they have to programs are built on ideas they have to
97.2s secondary to the ideas in the same way
97.2s secondary to the ideas in the same way programs are built on ideas they have to
100.1s programs are built on ideas they have to
100.2s programs are built on ideas they have to do something and what they're supposed do something and what they're supposed do something and what they're supposed to do I mean is like what writing is to do I mean is like what writing is to do I mean is like what writing is supposed to convey if people are trying
101.9s do something and what they're supposed
101.9s do something and what they're supposed to do I mean is like what writing is
104.8s to do I mean is like what writing is
104.8s to do I mean is like what writing is supposed to convey if people are trying
107.8s supposed to convey if people are trying supposed to convey if people are trying to learn programming by being taught to to learn programming by being taught to to learn programming by being taught to code well they're being taught writing code well they're being taught writing
107.8s supposed to convey if people are trying to learn programming by being taught to
110.3s to learn programming by being taught to
110.4s to learn programming by being taught to code well they're being taught writing
113.5s code well they're being taught writing
113.6s code well they're being taught writing by being taught how to type and that by being taught how to type and that by being taught how to type and that doesn't make much doesn't make much doesn't make much sense the best way way I have for sense the best way way I have for
116.0s by being taught how to type and that
116.0s by being taught how to type and that doesn't make much
118.2s doesn't make much
118.2s doesn't make much sense the best way way I have for
121.3s sense the best way way I have for
121.3s sense the best way way I have for teaching about programming as distinct teaching about programming as distinct teaching about programming as distinct from coding is to think about what the from coding is to think about what the from coding is to think about what the program is supposed to do mathematically program is supposed to do mathematically
123.7s teaching about programming as distinct
123.7s teaching about programming as distinct from coding is to think about what the
125.9s from coding is to think about what the
125.9s from coding is to think about what the program is supposed to do mathematically
128.7s program is supposed to do mathematically
128.8s program is supposed to do mathematically there's a very big practical problem there's a very big practical problem there's a very big practical problem with this the mathematical education in with this the mathematical education in with this the mathematical education in this country is pretty terrible most this country is pretty terrible most
131.0s there's a very big practical problem
131.0s there's a very big practical problem with this the mathematical education in
134.1s with this the mathematical education in
134.1s with this the mathematical education in this country is pretty terrible most
136.4s this country is pretty terrible most
136.4s this country is pretty terrible most people wind up being afraid of people wind up being afraid of people wind up being afraid of mathematics this is even senior mathematics this is even senior mathematics this is even senior programmers I've developed a language programmers I've developed a language
138.4s people wind up being afraid of
138.4s people wind up being afraid of mathematics this is even senior
141.2s mathematics this is even senior
141.2s mathematics this is even senior programmers I've developed a language
143.6s programmers I've developed a language
143.6s programmers I've developed a language called t for writing down the ideas called t for writing down the ideas called t for writing down the ideas that go into the program before before that go into the program before before that go into the program before before you do any coding it's a pretty hard
147.5s called t for writing down the ideas
147.5s called t for writing down the ideas that go into the program before before
150.0s that go into the program before before
150.0s that go into the program before before you do any coding it's a pretty hard
152.0s you do any coding it's a pretty hard you do any coding it's a pretty hard thing for engineers to get into but when thing for engineers to get into but when thing for engineers to get into but when they do it develops their ability to they do it develops their ability to
152.0s you do any coding it's a pretty hard thing for engineers to get into but when
155.1s thing for engineers to get into but when
155.1s thing for engineers to get into but when they do it develops their ability to
158.0s they do it develops their ability to
158.0s they do it develops their ability to think
173.7s mathematically a distributed system is mathematically a distributed system is one in which your computer can be one in which your computer can be one in which your computer can be rendered useless by the failure of a rendered useless by the failure of a rendered useless by the failure of a computer that you didn't even know
173.7s mathematically a distributed system is one in which your computer can be
177.8s one in which your computer can be
177.8s one in which your computer can be rendered useless by the failure of a
181.6s rendered useless by the failure of a
181.6s rendered useless by the failure of a computer that you didn't even know
183.4s computer that you didn't even know computer that you didn't even know existed non-distributed Computing is existed non-distributed Computing is existed non-distributed Computing is when different processes communicate by when different processes communicate by when different processes communicate by using the same memory and distributed using the same memory and distributed
183.4s computer that you didn't even know existed non-distributed Computing is
186.4s existed non-distributed Computing is
186.4s existed non-distributed Computing is when different processes communicate by
189.5s when different processes communicate by
189.5s when different processes communicate by using the same memory and distributed
192.3s using the same memory and distributed
192.4s using the same memory and distributed computing means that they're computing means that they're computing means that they're communicating with one another by communicating with one another by communicating with one another by sending messages now my interest in sending messages now my interest in sending messages now my interest in distributed systems came about by
194.8s computing means that they're
194.8s computing means that they're communicating with one another by
196.6s communicating with one another by
196.6s communicating with one another by sending messages now my interest in
200.1s sending messages now my interest in
200.1s sending messages now my interest in distributed systems came about by
203.1s distributed systems came about by distributed systems came about by Serendipity I received a pre-print of a Serendipity I received a pre-print of a Serendipity I received a pre-print of a paper by Robert Thomas and Paul Johnson paper by Robert Thomas and Paul Johnson paper by Robert Thomas and Paul Johnson who had an algorithm for implementing
203.1s distributed systems came about by Serendipity I received a pre-print of a
206.3s Serendipity I received a pre-print of a
206.4s Serendipity I received a pre-print of a paper by Robert Thomas and Paul Johnson
209.8s paper by Robert Thomas and Paul Johnson
209.8s paper by Robert Thomas and Paul Johnson who had an algorithm for implementing
211.9s who had an algorithm for implementing who had an algorithm for implementing distributed databases these are distributed databases these are distributed databases these are databases where you could have multiple databases where you could have multiple databases where you could have multiple copies of the data sitting at different copies of the data sitting at different
211.9s who had an algorithm for implementing distributed databases these are
213.9s distributed databases these are
214.0s distributed databases these are databases where you could have multiple
216.3s databases where you could have multiple
216.4s databases where you could have multiple copies of the data sitting at different
218.6s copies of the data sitting at different
218.6s copies of the data sitting at different computers so that programs on each computers so that programs on each computers so that programs on each computer could have rapid access to the computer could have rapid access to the computer could have rapid access to the data but they had to be synchronized so
221.0s computers so that programs on each
221.0s computers so that programs on each computer could have rapid access to the
223.3s computer could have rapid access to the
223.3s computer could have rapid access to the data but they had to be synchronized so
227.0s data but they had to be synchronized so data but they had to be synchronized so that processes on all the computers got that processes on all the computers got that processes on all the computers got consistent views of what the data was I consistent views of what the data was I
227.0s data but they had to be synchronized so that processes on all the computers got
230.2s that processes on all the computers got
230.2s that processes on all the computers got consistent views of what the data was I
233.2s consistent views of what the data was I
233.2s consistent views of what the data was I happened to have become quite familiar happened to have become quite familiar happened to have become quite familiar with special relativity one of the with special relativity one of the with special relativity one of the things that special relativity teachers things that special relativity teachers
235.8s happened to have become quite familiar
235.8s happened to have become quite familiar with special relativity one of the
237.8s with special relativity one of the
237.8s with special relativity one of the things that special relativity teachers
239.9s things that special relativity teachers
239.9s things that special relativity teachers you is that two different observers have you is that two different observers have you is that two different observers have different Notions of what at the same different Notions of what at the same different Notions of what at the same time means but there's one notion that
243.3s you is that two different observers have
243.3s you is that two different observers have different Notions of what at the same
245.9s different Notions of what at the same
245.9s different Notions of what at the same time means but there's one notion that
249.1s time means but there's one notion that time means but there's one notion that is invariant there's a certain notion of is invariant there's a certain notion of is invariant there's a certain notion of one event happening before another event one event happening before another event one event happening before another event and that means that it's possible for
249.2s time means but there's one notion that is invariant there's a certain notion of
251.9s is invariant there's a certain notion of
251.9s is invariant there's a certain notion of one event happening before another event
254.8s one event happening before another event
254.8s one event happening before another event and that means that it's possible for
258.1s and that means that it's possible for and that means that it's possible for information to be transmitted from one information to be transmitted from one information to be transmitted from one event to the other when the information event to the other when the information event to the other when the information cannot travel faster than the speed of
258.2s and that means that it's possible for information to be transmitted from one
261.3s information to be transmitted from one
261.3s information to be transmitted from one event to the other when the information
264.7s event to the other when the information
264.8s event to the other when the information cannot travel faster than the speed of
266.7s cannot travel faster than the speed of cannot travel faster than the speed of light I realized that that that notion light I realized that that that notion light I realized that that that notion of causality was violated by the of causality was violated by the of causality was violated by the algorithm of Thomas and Johnson it's
266.7s cannot travel faster than the speed of light I realized that that that notion
270.1s light I realized that that that notion
270.2s light I realized that that that notion of causality was violated by the
273.7s of causality was violated by the
273.8s of causality was violated by the algorithm of Thomas and Johnson it's
276.7s algorithm of Thomas and Johnson it's algorithm of Thomas and Johnson it's completely analogous to the relation and completely analogous to the relation and completely analogous to the relation and special relativity so what I did is I special relativity so what I did is I
276.7s algorithm of Thomas and Johnson it's completely analogous to the relation and
279.2s completely analogous to the relation and
279.2s completely analogous to the relation and special relativity so what I did is I
282.3s special relativity so what I did is I
282.3s special relativity so what I did is I wrote a paper that explained this notion wrote a paper that explained this notion wrote a paper that explained this notion of causality one could solve any of causality one could solve any of causality one could solve any distributed system Problem by building distributed system Problem by building
285.3s wrote a paper that explained this notion
285.3s wrote a paper that explained this notion of causality one could solve any
289.3s of causality one could solve any
289.3s of causality one could solve any distributed system Problem by building
293.1s distributed system Problem by building
293.2s distributed system Problem by building what I called a state machine think of what I called a state machine think of what I called a state machine think of it as an abstract computer that does one it as an abstract computer that does one
296.1s what I called a state machine think of
296.2s what I called a state machine think of it as an abstract computer that does one
298.6s it as an abstract computer that does one
298.6s it as an abstract computer that does one thing at a time you make sure that all thing at a time you make sure that all thing at a time you make sure that all the computers in this distributed system the computers in this distributed system the computers in this distributed system cooperate to implement a single state
302.1s thing at a time you make sure that all
302.1s thing at a time you make sure that all the computers in this distributed system
305.5s the computers in this distributed system
305.5s the computers in this distributed system cooperate to implement a single state
309.7s cooperate to implement a single state cooperate to implement a single state machine and that idea has become you machine and that idea has become you machine and that idea has become you know fundamental in the way people think know fundamental in the way people think know fundamental in the way people think about building distributed systems I had
309.7s cooperate to implement a single state machine and that idea has become you
313.8s machine and that idea has become you
313.8s machine and that idea has become you know fundamental in the way people think
317.0s know fundamental in the way people think
317.0s know fundamental in the way people think about building distributed systems I had
320.4s about building distributed systems I had about building distributed systems I had never even thought about a distributed never even thought about a distributed never even thought about a distributed system before I wrote that system before I wrote that system before I wrote that paper as I progressed in my career I
320.4s about building distributed systems I had never even thought about a distributed
322.1s never even thought about a distributed
322.1s never even thought about a distributed system before I wrote that
324.8s system before I wrote that
324.8s system before I wrote that paper as I progressed in my career I
328.6s paper as I progressed in my career I paper as I progressed in my career I came to appreciate of the idea of came to appreciate of the idea of came to appreciate of the idea of working in Industry that's where most of working in Industry that's where most of
328.6s paper as I progressed in my career I came to appreciate of the idea of
330.3s came to appreciate of the idea of
330.3s came to appreciate of the idea of working in Industry that's where most of
332.5s working in Industry that's where most of
332.5s working in Industry that's where most of the interesting problems that I found the interesting problems that I found the interesting problems that I found came from you know from Engineers having came from you know from Engineers having came from you know from Engineers having a problem to solve it reminds me a problem to solve it reminds me
334.3s the interesting problems that I found
334.3s the interesting problems that I found came from you know from Engineers having
336.9s came from you know from Engineers having
336.9s came from you know from Engineers having a problem to solve it reminds me
339.8s a problem to solve it reminds me
339.8s a problem to solve it reminds me actually of something that August Renoir actually of something that August Renoir actually of something that August Renoir once said if someone asked him why he once said if someone asked him why he once said if someone asked him why he painted outside rather than in his
342.5s actually of something that August Renoir
342.5s actually of something that August Renoir once said if someone asked him why he
345.7s once said if someone asked him why he
345.7s once said if someone asked him why he painted outside rather than in his
348.0s painted outside rather than in his painted outside rather than in his studio and what he said is if I were studio and what he said is if I were studio and what he said is if I were painting in the studio and I wanted to painting in the studio and I wanted to
348.0s painted outside rather than in his studio and what he said is if I were
350.3s studio and what he said is if I were
350.3s studio and what he said is if I were painting in the studio and I wanted to
352.1s painting in the studio and I wanted to
352.1s painting in the studio and I wanted to paint a leaf I would be able to you know paint a leaf I would be able to you know paint a leaf I would be able to you know think of only a half dozen or so think of only a half dozen or so
353.9s paint a leaf I would be able to you know
353.9s paint a leaf I would be able to you know think of only a half dozen or so
355.9s think of only a half dozen or so
355.9s think of only a half dozen or so different kinds of leaves that I could different kinds of leaves that I could different kinds of leaves that I could paint but when I was painting Outdoors paint but when I was painting Outdoors paint but when I was painting Outdoors there were just these millions of
357.3s different kinds of leaves that I could
357.3s different kinds of leaves that I could paint but when I was painting Outdoors
360.4s paint but when I was painting Outdoors
360.4s paint but when I was painting Outdoors there were just these millions of
362.2s there were just these millions of there were just these millions of different kinds of leaves that were different kinds of leaves that were different kinds of leaves that were there that I could paint there that I could paint there that I could paint from I found my research the same way
362.2s there were just these millions of different kinds of leaves that were
364.2s different kinds of leaves that were
364.2s different kinds of leaves that were there that I could paint
365.9s there that I could paint
365.9s there that I could paint from I found my research the same way
369.3s from I found my research the same way from I found my research the same way that if I sat down you know and just you that if I sat down you know and just you that if I sat down you know and just you know contemplated my Naval and think know contemplated my Naval and think
369.3s from I found my research the same way that if I sat down you know and just you
372.0s that if I sat down you know and just you
372.0s that if I sat down you know and just you know contemplated my Naval and think
374.1s know contemplated my Naval and think
374.1s know contemplated my Naval and think about problems you know there was this about problems you know there was this about problems you know there was this small number of problems that I could small number of problems that I could small number of problems that I could think of but there were just scars of
375.4s about problems you know there was this
375.4s about problems you know there was this small number of problems that I could
377.0s small number of problems that I could
377.0s small number of problems that I could think of but there were just scars of
379.4s think of but there were just scars of think of but there were just scars of them sitting out in Industry waiting to them sitting out in Industry waiting to them sitting out in Industry waiting to be to be solved my favorite of my be to be solved my favorite of my
379.4s think of but there were just scars of them sitting out in Industry waiting to
381.6s them sitting out in Industry waiting to
381.6s them sitting out in Industry waiting to be to be solved my favorite of my
384.8s be to be solved my favorite of my
384.8s be to be solved my favorite of my algorithms is the bakery algorithm it's algorithms is the bakery algorithm it's algorithms is the bakery algorithm it's to solve the mutual exclusion problem to solve the mutual exclusion problem to solve the mutual exclusion problem that is keep two processes from using that is keep two processes from using
387.6s algorithms is the bakery algorithm it's
387.6s algorithms is the bakery algorithm it's to solve the mutual exclusion problem
389.6s to solve the mutual exclusion problem
389.6s to solve the mutual exclusion problem that is keep two processes from using
391.7s that is keep two processes from using
391.7s that is keep two processes from using the printer at the same time processes the printer at the same time processes the printer at the same time processes choose a number based on the numbers choose a number based on the numbers choose a number based on the numbers that have been chosen by other processes
394.1s the printer at the same time processes
394.2s the printer at the same time processes choose a number based on the numbers
396.7s choose a number based on the numbers
396.7s choose a number based on the numbers that have been chosen by other processes
399.2s that have been chosen by other processes that have been chosen by other processes and use an algorithm so that the lowest and use an algorithm so that the lowest and use an algorithm so that the lowest is allowed to use the printer but what is allowed to use the printer but what
399.2s that have been chosen by other processes and use an algorithm so that the lowest
401.8s and use an algorithm so that the lowest
401.8s and use an algorithm so that the lowest is allowed to use the printer but what
403.6s is allowed to use the printer but what
403.6s is allowed to use the printer but what is amazing about it is it does not make is amazing about it is it does not make is amazing about it is it does not make an assumption that almost every other an assumption that almost every other an assumption that almost every other algorithm makes the Assumption being
407.4s is amazing about it is it does not make
407.4s is amazing about it is it does not make an assumption that almost every other
410.1s an assumption that almost every other
410.1s an assumption that almost every other algorithm makes the Assumption being
412.7s algorithm makes the Assumption being algorithm makes the Assumption being that if say I'm changing my number from that if say I'm changing my number from that if say I'm changing my number from 47 to 100 and you read that number 47 to 100 and you read that number
412.8s algorithm makes the Assumption being that if say I'm changing my number from
415.9s that if say I'm changing my number from
416.0s that if say I'm changing my number from 47 to 100 and you read that number
419.6s 47 to 100 and you read that number
419.6s 47 to 100 and you read that number you'll either get 47 or 100 but that you'll either get 47 or 100 but that you'll either get 47 or 100 but that algorithm works even if instead of algorithm works even if instead of algorithm works even if instead of getting 47 or 100 you maybe got 4700 or
422.6s you'll either get 47 or 100 but that
422.6s you'll either get 47 or 100 but that algorithm works even if instead of
424.6s algorithm works even if instead of
424.6s algorithm works even if instead of getting 47 or 100 you maybe got 4700 or
428.4s getting 47 or 100 you maybe got 4700 or getting 47 or 100 you maybe got 4700 or maybe you got maybe you got maybe you got 99,999 the algorithm still works I 99,999 the algorithm still works I 99,999 the algorithm still works I didn't intend it to I mean I didn't
428.4s getting 47 or 100 you maybe got 4700 or maybe you got
431.0s maybe you got
431.0s maybe you got 99,999 the algorithm still works I
434.5s 99,999 the algorithm still works I
434.5s 99,999 the algorithm still works I didn't intend it to I mean I didn't
436.1s didn't intend it to I mean I didn't didn't intend it to I mean I didn't intend that I just discovered that when intend that I just discovered that when intend that I just discovered that when I wrote a proof I never needed to make I wrote a proof I never needed to make
436.2s didn't intend it to I mean I didn't intend that I just discovered that when
438.3s intend that I just discovered that when
438.3s intend that I just discovered that when I wrote a proof I never needed to make
440.7s I wrote a proof I never needed to make
440.8s I wrote a proof I never needed to make the assumption that is just so the assumption that is just so the assumption that is just so beautiful uh and you know I'm really beautiful uh and you know I'm really beautiful uh and you know I'm really proud that that that I uh stumbled on it
443.4s the assumption that is just so
443.4s the assumption that is just so beautiful uh and you know I'm really
448.1s beautiful uh and you know I'm really
448.2s beautiful uh and you know I'm really proud that that that I uh stumbled on it
453.4s proud that that that I uh stumbled on it proud that that that I uh stumbled on it Music
453.4s proud that that that I uh stumbled on it Music