Breaking Math Podcast
http://www.brilliant.org/breakingmath
Fri, 13 Apr 2018 17:07:07 +0000Fri, 13 Apr 2018 17:07:07 +000060enAll rights reservedfeeds@soundcloud.com (SoundCloud Feeds)Breaking Math is a podcast that aims to make math accessible to everyone, and make it enjoyable. Every other week, topics such as chaos theory, forbidden formulas, and more will be covered in detail. If you have 45 or so minutes to spare, you're almost guaranteed to learn something new!Breaking Math is a podcast that aims to make math…Breaking Math Podcastbreakingmathpodcast@gmail.comBreaking Mathnohttp://i1.sndcdn.com/avatars-000293465751-8vd3lf-original.jpgBreaking Math Podcast
http://www.brilliant.org/breakingmath
tag:soundcloud,2010:tracks/42924025525: Pandemic PanicFri, 13 Apr 2018 17:06:26 +0000
https://soundcloud.com/breakingmathpodcast/25-pandemic-panic
00:44:34Breaking MathnoThe spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?The spectre of disease causes untold mayhem, angu…The spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?tag:soundcloud,2010:tracks/40990407624: Language and EntropyWed, 07 Mar 2018 06:27:12 +0000
https://soundcloud.com/breakingmathpodcast/24-language-and-entropy
00:45:06Breaking MathnoInformation theory was founded in 1948 by Claude Shannon, and is a way of both qualitatively and quantitatively describing the limits and processes involved in communication. Roughly speaking, when two entities communicate, they have a message, a medium, confusion, encoding, and decoding; and when two entities communicate, they transfer information between them. The amount of information that is possible to be transmitted can be increased or decreased by manipulating any of the aforementioned variables. One of the practical, and original, applications of information theory is to models of language. So what is entropy? How can we say language has it? And what structures within language with respect to information theory reveal deep insights about the nature of language itself?Information theory was founded in 1948 by Claude …Information theory was founded in 1948 by Claude Shannon, and is a way of both qualitatively and quantitatively describing the limits and processes involved in communication. Roughly speaking, when two entities communicate, they have a message, a medium, confusion, encoding, and decoding; and when two entities communicate, they transfer information between them. The amount of information that is possible to be transmitted can be increased or decreased by manipulating any of the aforementioned variables. One of the practical, and original, applications of information theory is to models of language. So what is entropy? How can we say language has it? And what structures within language with respect to information theory reveal deep insights about the nature of language itself?tag:soundcloud,2010:tracks/405088395Stay Tuned for Season 2!Sun, 25 Feb 2018 20:31:32 +0000
https://soundcloud.com/breakingmathpodcast/stay-tuned-for-season-2
00:00:32Breaking MathnoJonathan and Gabriel discuss what you have to expect with Breaking Math's second season!Jonathan and Gabriel discuss what you have to exp…Jonathan and Gabriel discuss what you have to expect with Breaking Math's second season!tag:soundcloud,2010:tracks/38400876523: Don't Touch My Circles!Mon, 15 Jan 2018 17:55:39 +0000
https://soundcloud.com/breakingmathpodcast/23-dont-touch-my-circles
00:52:40Breaking MathnoIn the study of mathematics, there are many abstractions that we deal with. For example, we deal with the notion of a real number with infinitesimal granularity and infinite range, even though we have no evidence for this existing in nature besides the generally noted demi-rules 'smaller things keep getting discovered' and 'larger things keep getting discovered'. In a similar fashion, we define things like circles, squares, lines, planes, and so on. Many of the concepts that were just mentioned have to do with geometry; and perhaps it is because our brains developed to deal with geometric information, or perhaps it is because geometry is the language of nature, but there's no doubt denying that geometry is one of the original forms of mathematics. So what defines geometry? Can we make progress indefinitely with it? And where is the line between geometry and analysis?In the study of mathematics, there are many abstr…In the study of mathematics, there are many abstractions that we deal with. For example, we deal with the notion of a real number with infinitesimal granularity and infinite range, even though we have no evidence for this existing in nature besides the generally noted demi-rules 'smaller things keep getting discovered' and 'larger things keep getting discovered'. In a similar fashion, we define things like circles, squares, lines, planes, and so on. Many of the concepts that were just mentioned have to do with geometry; and perhaps it is because our brains developed to deal with geometric information, or perhaps it is because geometry is the language of nature, but there's no doubt denying that geometry is one of the original forms of mathematics. So what defines geometry? Can we make progress indefinitely with it? And where is the line between geometry and analysis?tag:soundcloud,2010:tracks/37365072822: IncompletSat, 23 Dec 2017 23:43:29 +0000
https://soundcloud.com/breakingmathpodcast/22-incomplet
00:56:31Breaking MathnoGödel, Escher, Bach is a book about everything from formal logic to the intricacies underlying the mechanisms of reasoning. For that reason, we've decided to make a tribute episode; specifically, about episode IV. There is a Sanskrit word "maya" which describes the difference between a symbol and that which it symbolizes. This episode is going to be all about the math of maya. So what is a string? How are formal systems useful? And why do we study them with such vigor?Gödel, Escher, Bach is a book about everything fr…Gödel, Escher, Bach is a book about everything from formal logic to the intricacies underlying the mechanisms of reasoning. For that reason, we've decided to make a tribute episode; specifically, about episode IV. There is a Sanskrit word "maya" which describes the difference between a symbol and that which it symbolizes. This episode is going to be all about the math of maya. So what is a string? How are formal systems useful? And why do we study them with such vigor?tag:soundcloud,2010:tracks/36502587821: Einstein's Biggest IdeaMon, 04 Dec 2017 22:53:22 +0000
https://soundcloud.com/breakingmathpodcast/21-einsteins-biggest-idea
01:02:38Breaking MathnoSome see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by experiment, general relativity gives us a framework for understanding not only the relationship between mass and energy and space and time, but topology and destiny. So why is relativity such an important concept? How do special and general relativity differ? And what is meant by the equation G=8πT?Some see the world of thought divided into two ty…Some see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by experiment, general relativity gives us a framework for understanding not only the relationship between mass and energy and space and time, but topology and destiny. So why is relativity such an important concept? How do special and general relativity differ? And what is meant by the equation G=8πT?tag:soundcloud,2010:tracks/35743653520: RationalSat, 18 Nov 2017 04:52:59 +0000
https://soundcloud.com/breakingmathpodcast/rational
00:40:22Breaking MathnoFrom MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?From MC²’s statement of mass energy equivalence a…From MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?tag:soundcloud,2010:tracks/35222682219: Tune of the Hickory StickTue, 07 Nov 2017 03:39:30 +0000
https://soundcloud.com/breakingmathpodcast/19-tune-of-the-hickory-stick
00:39:51Breaking MathnoFrom MC2’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?From MC2’s statement of mass energy equivalence a…From MC2’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?tag:soundcloud,2010:tracks/34645046218: FrequencyWed, 11 Oct 2017 19:58:22 +0000
https://soundcloud.com/breakingmathpodcast/18-frequency
00:44:05Breaking MathnoDuration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they been studied? And how do they relate to the rest of mathematics?Duration and proximity are, as demonstrated by Fo…Duration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they been studied? And how do they relate to the rest of mathematics?tag:soundcloud,2010:tracks/34542092617: Navier StokedThu, 05 Oct 2017 02:02:51 +0000
https://soundcloud.com/breakingmathpodcast/17-navier-stoked
01:00:24Breaking MathnoFrom our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others as more statistical, but by all as a challenge. This definition cannot fit into an introduction, and I’ll be picking away at it for the remainder of this episode. So what is a fluid? What can we learn from it? And how could learning from it be worth a million dollars?From our first breath of the day to brushing our …From our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others as more statistical, but by all as a challenge. This definition cannot fit into an introduction, and I’ll be picking away at it for the remainder of this episode. So what is a fluid? What can we learn from it? And how could learning from it be worth a million dollars?tag:soundcloud,2010:tracks/343003014BFNB2: Thought for FoodTue, 19 Sep 2017 03:57:17 +0000
https://soundcloud.com/breakingmathpodcast/bfnb2-thought-for-food
01:09:41Breaking MathnoSponsored by www.brilliant.org/breakingmath, where you can take courses in calculus, computer science, chemistry, and other STEM subjects. All online; all at your own pace; and accessible anywhere with an internet connection, including your smartphone or tablet! Start learning today!
Check out: https://blankfornonblank.podiant.co/e/357f09da787bac/
What you're about to hear is part two of an episode recorded by the podcasting network ___forNon___ (Blank for Non-Blank), of which Breaking Math, along with several other podcasts, is a part. To check out more ___forNon___ content, you can click on the link in this description. And of course, for more info and interactive widgets you can go to breakingmathpodcast.com, you can support us at patreon.com/breakingmathpodcast, and you can contact us directly at breakingmathpodcast@gmail.com. We hope you enjoy the second part of the first ___forNon___ group episode. You can also support ___forNon___ by donating at patreon.com/blankfornonblank.Sponsored by www.brilliant.org/breakingmath, wher…Sponsored by www.brilliant.org/breakingmath, where you can take courses in calculus, computer science, chemistry, and other STEM subjects. All online; all at your own pace; and accessible anywhere with an internet connection, including your smartphone or tablet! Start learning today!
Check out: https://blankfornonblank.podiant.co/e/357f09da787bac/
What you're about to hear is part two of an episode recorded by the podcasting network ___forNon___ (Blank for Non-Blank), of which Breaking Math, along with several other podcasts, is a part. To check out more ___forNon___ content, you can click on the link in this description. And of course, for more info and interactive widgets you can go to breakingmathpodcast.com, you can support us at patreon.com/breakingmathpodcast, and you can contact us directly at breakingmathpodcast@gmail.com. We hope you enjoy the second part of the first ___forNon___ group episode. You can also support ___forNon___ by donating at patreon.com/blankfornonblank.tag:soundcloud,2010:tracks/342578111BFNB1: Food for ThoughtSat, 16 Sep 2017 02:31:37 +0000
https://soundcloud.com/breakingmathpodcast/bfnb1-food-for-thought
00:33:38Breaking MathnoThis is the first group podcast for the podcasting network ___forNon___ (pronounced "Blank for Non-Blank"), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode.This is the first group podcast for the podcastin…This is the first group podcast for the podcasting network ___forNon___ (pronounced "Blank for Non-Blank"), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode.tag:soundcloud,2010:tracks/340655392A Special MessageSat, 02 Sep 2017 23:47:18 +0000
https://soundcloud.com/breakingmathpodcast/a-special-message
00:01:01Breaking MathnoHello. This is Jonathan from Breaking Math to bring you a special
message. Gabriel, my co-host, has recently had a child. The child
is healthy, but both children and Breaking Math take time,
and we're still figuring out how to make use of said time most
efficiently. So I'm here to tell you what you can expect in the
mean time.
In the mean time, you can expect some minisodes from us. These will
be covering a variety of topics, hopefully including the millennium
problems.
You can also expect us to release new episodes again in a very short
amount of time. The hosts and their families have discussed how time
is going to be spent, and all that remains to be seen is if this plan
is realistic, and to tweak it to make sure that you all get the same
content you've grown to know and love.
So thank you all for your patience, and if you have anything to say
to us in the mean time, you can write to us at breakingmathpodcast@gmail.com
or write to us on our facebook page, which is at facebook.com/breakingmathpodcast.
Thank you, and until we see you again, don't forget to check
periodically for updates of Breaking Math. Bye!Hello. This is Jonathan from Breaking Math to bri…Hello. This is Jonathan from Breaking Math to bring you a special
message. Gabriel, my co-host, has recently had a child. The child
is healthy, but both children and Breaking Math take time,
and we're still figuring out how to make use of said time most
efficiently. So I'm here to tell you what you can expect in the
mean time.
In the mean time, you can expect some minisodes from us. These will
be covering a variety of topics, hopefully including the millennium
problems.
You can also expect us to release new episodes again in a very short
amount of time. The hosts and their families have discussed how time
is going to be spent, and all that remains to be seen is if this plan
is realistic, and to tweak it to make sure that you all get the same
content you've grown to know and love.
So thank you all for your patience, and if you have anything to say
to us in the mean time, you can write to us at breakingmathpodcast@gmail.com
or write to us on our facebook page, which is at facebook.com/breakingmathpodcast.
Thank you, and until we see you again, don't forget to check
periodically for updates of Breaking Math. Bye!tag:soundcloud,2010:tracks/338471222Minisode 0.6: Four ProblemsFri, 18 Aug 2017 20:00:23 +0000
https://soundcloud.com/breakingmathpodcast/minisode-06-four-problems
00:24:13Breaking MathnoJonathan and Gabriel discuss four challenging problems.Jonathan and Gabriel discuss four challenging pro…Jonathan and Gabriel discuss four challenging problems.tag:soundcloud,2010:tracks/33546665415: Consciousness ISun, 30 Jul 2017 03:50:22 +0000
https://soundcloud.com/breakingmathpodcast/15-consciousness-i
01:00:42Breaking MathnoWhat does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we seem to be closer than ever to revealing aspects of consciousness that we’ve never beheld. So what does it mean to feel? What are qualia? And how do we know that we ourselves are conscious?What does it mean to be a good person? What does …What does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we seem to be closer than ever to revealing aspects of consciousness that we’ve never beheld. So what does it mean to feel? What are qualia? And how do we know that we ourselves are conscious?tag:soundcloud,2010:tracks/333976986Minisode 0.5: ___forNon___Thu, 20 Jul 2017 04:25:19 +0000
https://soundcloud.com/breakingmathpodcast/minisode-05-fornon
00:12:17Breaking MathnoJonathan and Gabriel discuss ___forNon___ (blank for non-blank); a podcasting collective they've recently joined. Check out more at blankfornonblank.com.Jonathan and Gabriel discuss ___forNon___ (blank …Jonathan and Gabriel discuss ___forNon___ (blank for non-blank); a podcasting collective they've recently joined. Check out more at blankfornonblank.com.tag:soundcloud,2010:tracks/33259018714: Artificial ThoughtTue, 11 Jul 2017 00:05:11 +0000
https://soundcloud.com/breakingmathpodcast/breakingmath14-final
01:05:38Breaking MathnoGo to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math.
Mathematics takes inspiration from all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have their origins around the time of automated computing, and with advances in hardware, have advanced in turn. So what is a neuron? How do multitudes of them contribute to structured thought? And what is in their future?Go to www.brilliant.org/breakingmathpodcast to le…Go to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math.
Mathematics takes inspiration from all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have their origins around the time of automated computing, and with advances in hardware, have advanced in turn. So what is a neuron? How do multitudes of them contribute to structured thought? And what is in their future?tag:soundcloud,2010:tracks/33028001713: Math and Prison RiotsTue, 27 Jun 2017 01:45:48 +0000
https://soundcloud.com/breakingmathpodcast/13-math-and-prison-riots
00:49:01Breaking MathnoFrank Salas is an statistical exception, but far from an irreplicable result. Busted on the streets of Albuquerque for selling crack cocaine at 17, an age where many of us are busy honing the skills that we've chosen to master, and promply incarcerated in one of the myriad concrete boxes that comprise the United States penal system. There, he struggled, as most would in his position, to better himself spiritually or ethically, once even participating in a prison riot. After two stints in solitary confinement, he did the unthinkable: he imagined a better world for himself. One where it was not all him versus the world. With newfound vigor, he discovered what was there all along: a passion for mathematics and the sciences. After nine years of hard time he graduated to a halfway house. From there, we attended classes at community college, honing his skills using his second lease on life. That took him on a trajectory which developed into him working on a PhD in electrical engineering from the University of Michegan. We're talking, of course, about Frank Salas; a man who is living proof that condition and destiny are not forced to correlate, and who uses this proof as inspiration for many in the halway house that he once roamed. So who is he? What is his mission? And who is part of that mission? And what does this have to do with Maxwell's equations of electromagnetism?Frank Salas is an statistical exception, but far …Frank Salas is an statistical exception, but far from an irreplicable result. Busted on the streets of Albuquerque for selling crack cocaine at 17, an age where many of us are busy honing the skills that we've chosen to master, and promply incarcerated in one of the myriad concrete boxes that comprise the United States penal system. There, he struggled, as most would in his position, to better himself spiritually or ethically, once even participating in a prison riot. After two stints in solitary confinement, he did the unthinkable: he imagined a better world for himself. One where it was not all him versus the world. With newfound vigor, he discovered what was there all along: a passion for mathematics and the sciences. After nine years of hard time he graduated to a halfway house. From there, we attended classes at community college, honing his skills using his second lease on life. That took him on a trajectory which developed into him working on a PhD in electrical engineering from the University of Michegan. We're talking, of course, about Frank Salas; a man who is living proof that condition and destiny are not forced to correlate, and who uses this proof as inspiration for many in the halway house that he once roamed. So who is he? What is his mission? And who is part of that mission? And what does this have to do with Maxwell's equations of electromagnetism?tag:soundcloud,2010:tracks/32778936712: Math FactoryTue, 13 Jun 2017 00:28:42 +0000
https://soundcloud.com/breakingmathpodcast/12-math-factory
00:50:44Breaking MathnoIn a universe where everything is representable by information, what does it mean to interact with that world? When you follow a series of steps to accomplish a goal, what you're doing is taking part in a mathematical tradition as old as math itself: algorithms. From time immemorial, we've accelerated the growth of this means of transformation, and whether we're modeling neurons, recognizing faces, designing trusses on a bridge, or coloring a map, we're involving ourselves heavily in a fantastic world, where everything is connected to everything else through a massive network of mathematical factories. So does it mean to do something? What does it mean for something to end? And what is time relative to these questions?In a universe where everything is representable b…In a universe where everything is representable by information, what does it mean to interact with that world? When you follow a series of steps to accomplish a goal, what you're doing is taking part in a mathematical tradition as old as math itself: algorithms. From time immemorial, we've accelerated the growth of this means of transformation, and whether we're modeling neurons, recognizing faces, designing trusses on a bridge, or coloring a map, we're involving ourselves heavily in a fantastic world, where everything is connected to everything else through a massive network of mathematical factories. So does it mean to do something? What does it mean for something to end? And what is time relative to these questions?tag:soundcloud,2010:tracks/32529503111: A Culture of HackingWed, 31 May 2017 02:17:58 +0000
https://soundcloud.com/breakingmathpodcast/11-a-culture-of-hacking
00:59:59Breaking MathnoThe culture of mathematics is a strange topic. It is almost as important to the history of mathematics as the theorems that have come from it, yet it is rarely commented upon, and it is almost never taught in schools. One form of mathematical inquiry that has cropped up in the last two centuries has been the algorithm. While not exclusive to this time period, it has achieved a renaissance, and with the algorithm has come what has come to be known as "hacker culture". From Lord Byron to Richard Stallman, from scratches on paper to masses of wire, hacker culture has influenced the way in which we interact with conveniences that algorithms have endowed upon our society. So what are these advances? How have they been affected by the culture which birthed them? And what can we learn from this fragile yet pervasive relationship?The culture of mathematics is a strange topic. It…The culture of mathematics is a strange topic. It is almost as important to the history of mathematics as the theorems that have come from it, yet it is rarely commented upon, and it is almost never taught in schools. One form of mathematical inquiry that has cropped up in the last two centuries has been the algorithm. While not exclusive to this time period, it has achieved a renaissance, and with the algorithm has come what has come to be known as "hacker culture". From Lord Byron to Richard Stallman, from scratches on paper to masses of wire, hacker culture has influenced the way in which we interact with conveniences that algorithms have endowed upon our society. So what are these advances? How have they been affected by the culture which birthed them? And what can we learn from this fragile yet pervasive relationship?tag:soundcloud,2010:tracks/32284471910: CryptomathTue, 16 May 2017 05:02:01 +0000
https://soundcloud.com/breakingmathpodcast/10-cryptomath
01:14:19Breaking MathnoLanguage and communication is a huge part of what it means to be a person, and a large part of this importance is the ability to direct the flow of that information; this is a practice known as cryptography. There are as many ways to encrypt data as there are ways to use them, ranging from cryptoquips solvable by children in an afternoon to four kilobit RSA taking eons of time. So why are there so many forms of encryption? What can they be used for? And what are the differences in their methodology, if not philosophy?Language and communication is a huge part of what…Language and communication is a huge part of what it means to be a person, and a large part of this importance is the ability to direct the flow of that information; this is a practice known as cryptography. There are as many ways to encrypt data as there are ways to use them, ranging from cryptoquips solvable by children in an afternoon to four kilobit RSA taking eons of time. So why are there so many forms of encryption? What can they be used for? And what are the differences in their methodology, if not philosophy?tag:soundcloud,2010:tracks/3204580959: Humanity 2.0Tue, 02 May 2017 06:02:04 +0000
https://soundcloud.com/breakingmathpodcast/9-humanity-20
00:52:08Breaking MathnoHumanity, since its inception, has been nebulously defined. Every technological advancement has changed what it means to be a person, and every person has changed what it means to advance. In this same vein, there is a concept called “transhumanism”, which refers to what it will mean to be a person. This can range from everything from genetic engineering, to artificial intelligence, to technology which is beyond our current physical understanding. So what does it mean to be a person? And is transhumanism compatible with our natural understanding, if it exists, of being?Humanity, since its inception, has been nebulousl…Humanity, since its inception, has been nebulously defined. Every technological advancement has changed what it means to be a person, and every person has changed what it means to advance. In this same vein, there is a concept called “transhumanism”, which refers to what it will mean to be a person. This can range from everything from genetic engineering, to artificial intelligence, to technology which is beyond our current physical understanding. So what does it mean to be a person? And is transhumanism compatible with our natural understanding, if it exists, of being?tag:soundcloud,2010:tracks/320274746Minisode 0.4: Comin' Up NextMon, 01 May 2017 02:51:40 +0000
https://soundcloud.com/breakingmathpodcast/minisode-04-comin-up-next
00:13:56Breaking MathnoJonathan and Gabriel talk about the next four episodes coming down the pike, including Humanity 2.0, which debuts Tuesday, April 2nd 2017.Jonathan and Gabriel talk about the next four epi…Jonathan and Gabriel talk about the next four episodes coming down the pike, including Humanity 2.0, which debuts Tuesday, April 2nd 2017.tag:soundcloud,2010:tracks/318693321Minisode 0.3: Lights, Camera, Action!Thu, 20 Apr 2017 20:31:09 +0000
https://soundcloud.com/breakingmathpodcast/minisode-03-lights-camera-action
00:17:48Breaking MathnoJonathan and Gabriel discuss their recent news debut! You can find what they're talking about at news.unm.eduJonathan and Gabriel discuss their recent news de…Jonathan and Gabriel discuss their recent news debut! You can find what they're talking about at news.unm.edutag:soundcloud,2010:tracks/3182074378: Evolution and EngineeringTue, 18 Apr 2017 06:00:28 +0000
https://soundcloud.com/breakingmathpodcast/8-evolution-and-engineering
00:57:39Breaking MathnoComputation is a nascent science, and as such, looks towards the other sciences for inspiration. Whether it be physics, as in simulated annealing, or, as now is popular, biology, as in neural networks, computer science has shown repeatedly that it can learn great things from other sciences. Genetic algorithms are one such method that is inspired, of course, by biological evolution. So what are genetic algorithms used for? What have they taught us about the natural process of evolution? And how can we use them to improve our world?Computation is a nascent science, and as such, lo…Computation is a nascent science, and as such, looks towards the other sciences for inspiration. Whether it be physics, as in simulated annealing, or, as now is popular, biology, as in neural networks, computer science has shown repeatedly that it can learn great things from other sciences. Genetic algorithms are one such method that is inspired, of course, by biological evolution. So what are genetic algorithms used for? What have they taught us about the natural process of evolution? And how can we use them to improve our world?tag:soundcloud,2010:tracks/317097309Minisode 0.2: What's Up, Bangalore?Mon, 10 Apr 2017 23:04:56 +0000
https://soundcloud.com/breakingmathpodcast/whats-up-bangalore
00:26:37Breaking MathnoJonathan and Gabriel discuss everything Bangalore, evolutionary algorithmic, and more!Jonathan and Gabriel discuss everything Bangalore…Jonathan and Gabriel discuss everything Bangalore, evolutionary algorithmic, and more!tag:soundcloud,2010:tracks/3160192077: QED? Prove it.Tue, 04 Apr 2017 07:18:27 +0000
https://soundcloud.com/breakingmathpodcast/7-qed-prove-it
00:44:03Breaking MathnoProofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it?Proofs are sometimes seen as an exercise in tediu…Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it?tag:soundcloud,2010:tracks/315616447Minisode 0.1: Hypercubes and Other Stranger ThingsSat, 01 Apr 2017 22:53:18 +0000
https://soundcloud.com/breakingmathpodcast/01-hypercube-and-other-stranger-things
00:22:08Breaking MathnoWe are proud to announce that we have recorded our very first minisode! In addition, we are introducing a new blog which can be found at www.breakingmathpodcast.com/blog.htmlWe are proud to announce that we have recorded ou…We are proud to announce that we have recorded our very first minisode! In addition, we are introducing a new blog which can be found at www.breakingmathpodcast.com/blog.htmltag:soundcloud,2010:tracks/3135635766: WordTue, 21 Mar 2017 06:00:09 +0000
https://soundcloud.com/breakingmathpodcast/6-word
00:49:35Breaking MathnoMathematics has a lot in common with language. Both have been used since the dawn of time to shape and define our world, both have sets of rules which one must master before bending, both are natural consequences of the way humans are raised, and both are as omnipresent as they are seemingly intangible. Language has thrived for almost, or as long as humans have possessed the ability to use it. But what can we say that language is? Is it a living breathing organism, a set of rigid ideals, somewhere in between, or something else altogether?Mathematics has a lot in common with language. Bo…Mathematics has a lot in common with language. Both have been used since the dawn of time to shape and define our world, both have sets of rules which one must master before bending, both are natural consequences of the way humans are raised, and both are as omnipresent as they are seemingly intangible. Language has thrived for almost, or as long as humans have possessed the ability to use it. But what can we say that language is? Is it a living breathing organism, a set of rigid ideals, somewhere in between, or something else altogether?tag:soundcloud,2010:tracks/3111359105: Language of the UniverseTue, 07 Mar 2017 07:15:11 +0000
https://soundcloud.com/breakingmathpodcast/5-language-of-the-universe
00:48:13Breaking Mathno1948. A flash, followed by an explosion. Made possible by months of mathematical computation, the splitting of the atom was hailed as a triumph of both science and mathematics. Mathematics is seen by many as a way of quantifying experiments. But is that always the case? There are cases where it seems as though mathematics itself has made predictions about the universe and vice versa. So how are these predictions made? And what can we learn about both physics and math by examining the way in which these topics intermingle?1948. A flash, followed by an explosion. Made pos…1948. A flash, followed by an explosion. Made possible by months of mathematical computation, the splitting of the atom was hailed as a triumph of both science and mathematics. Mathematics is seen by many as a way of quantifying experiments. But is that always the case? There are cases where it seems as though mathematics itself has made predictions about the universe and vice versa. So how are these predictions made? And what can we learn about both physics and math by examining the way in which these topics intermingle?tag:soundcloud,2010:tracks/3087917164: Digital EvolutionTue, 21 Feb 2017 07:04:06 +0000
https://soundcloud.com/breakingmathpodcast/digital-evolution
00:52:41Breaking MathnoWe live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in“We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in bone to signals zipping by at almost the speed of light, our endeavors as humans, and some argue, our existence in the universe, is ruled by the concept of digital information. So how did we discover digital information? And what has it been used for?We live in an era of unprecedented change, and th…We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in“We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in bone to signals zipping by at almost the speed of light, our endeavors as humans, and some argue, our existence in the universe, is ruled by the concept of digital information. So how did we discover digital information? And what has it been used for?tag:soundcloud,2010:tracks/3065451603: TMITue, 07 Feb 2017 14:27:27 +0000
https://soundcloud.com/breakingmathpodcast/3-tmi
00:46:23Breaking Mathno“ABABABABABABABAB”. How much information was that? You may say “sixteen letters worth”, but is that the true answer? You could describe what you just read as “AB 8 times”, and save a bunch of characters, and yet have the same information. But what is information in the context of mathematics? The answer is nothing short of miraculous; information theory has applications in telephony, human language, and even physics. So what is information theory, and what can we learn from it?“ABABABABABABABAB”. How much information was that…“ABABABABABABABAB”. How much information was that? You may say “sixteen letters worth”, but is that the true answer? You could describe what you just read as “AB 8 times”, and save a bunch of characters, and yet have the same information. But what is information in the context of mathematics? The answer is nothing short of miraculous; information theory has applications in telephony, human language, and even physics. So what is information theory, and what can we learn from it?tag:soundcloud,2010:tracks/3065447232: Wreaking ChaosTue, 07 Feb 2017 14:23:43 +0000
https://soundcloud.com/breakingmathpodcast/2-wreaking-chaos
00:51:44Breaking MathnoThe void has always intrigued mankind; the concept of no concept defies the laws of human reasoning to such a degree that we have no choice but to pursue it. But ancient Assyrian, Norse, Judeo-Christian creation stories, and even our own scientific inquiries have one thing in common: creation from “nothingness”. But is it really nothingness? The ancients used the term “chaos”, and, although to some “chaos” has become synonymous with “bedlam” or “randomness”, it has much more to do with the timeless myths of creation of form from the formless. So how does chaos take form? And is there meaning to be found in the apparent arbitrariness of chaos, or is it a void that defines what we think it means to be?The void has always intrigued mankind; the concep…The void has always intrigued mankind; the concept of no concept defies the laws of human reasoning to such a degree that we have no choice but to pursue it. But ancient Assyrian, Norse, Judeo-Christian creation stories, and even our own scientific inquiries have one thing in common: creation from “nothingness”. But is it really nothingness? The ancients used the term “chaos”, and, although to some “chaos” has become synonymous with “bedlam” or “randomness”, it has much more to do with the timeless myths of creation of form from the formless. So how does chaos take form? And is there meaning to be found in the apparent arbitrariness of chaos, or is it a void that defines what we think it means to be?tag:soundcloud,2010:tracks/3065441611: Forbidden FormulasTue, 07 Feb 2017 14:19:28 +0000
https://soundcloud.com/breakingmathpodcast/1-forbidden-formulas
00:59:27Breaking MathnoFrom Pythagoras to Einstein, from the banks of the Nile to the streamlined curves of the Large Hadron Collider, math has shown itself again and again to be fundamental to the way that humans interact with the world. Then why is math such a pain for so many people? Our answer is simple: math is, and always has been, in one way or another, guarded as an elite skill. We visit the worlds that were shaped by math, the secrets people died for, the false gods created through this noble science, and the gradual chipping away of this knowledge by a people who have always yearned for this magical skill. So what is it? And how can we make it better?From Pythagoras to Einstein, from the banks of th…From Pythagoras to Einstein, from the banks of the Nile to the streamlined curves of the Large Hadron Collider, math has shown itself again and again to be fundamental to the way that humans interact with the world. Then why is math such a pain for so many people? Our answer is simple: math is, and always has been, in one way or another, guarded as an elite skill. We visit the worlds that were shaped by math, the secrets people died for, the false gods created through this noble science, and the gradual chipping away of this knowledge by a people who have always yearned for this magical skill. So what is it? And how can we make it better?