Sunday, July 25, 2010
Ein bischen Deutsch...
Und heute hab ich Lust eine Post auf Deutsch zu schreiben. Auf jeden fall ist mein Grammatisch und Wort-benutzung sehr schlecht aber manchmal denke ich dass ein bischen schreiben auf Deutsch konnte die fremdsprach fur mich verbessern. Fremdsprach ist so wichtig ein Kunst zu lernen, besonders fur Amerikaner. Wir besetzen hier an diese grosse Kontinent mit sehr wenig kulturisch verschieden. Damit die ganze Welt zu verstanden, mussten wir weit und breit reisen zu Fremdkultur zu finden. Wenn dies moglichkeit besetzt uns, wir sollten bereits werden. Mit die Landessprach vermitteln ist am besten weg die richtige Volkskultur zu tragen. Sprachforschung untericht viel uber die Kulture eine Lande. Ich hoffe das ich vergess dies Fremdsprach nicht und ich weiss das ich muss immer benutzen zu mir errinern. Vielleicht fang ich ein sprach-wechseln mit Skype eines Tages an. Und hoffenlich kann ich am endlich nach Deutschland Rueckreise.
Friday, July 9, 2010
Rigor in Development: How open-source science can improve our world
What am I reading today?
Mathematics: The Loss of Certainty
By, Morris Kline
Not a book you should pick up for an easy read on a road trip to Disney World, but "Mathematics: The Loss of Certainty" goes through the invention of Mathematics from its roots with the Babylonians back in 3000 BC to the Greeks creation of Euclidian geometry to the quarrels and debates of its development that lasted through the 19th century and on to today. It's interesting to see how some of the most useful mathematical methods like negative numbers, the complex number system, and irrationals, were hotly debated topics for hundreds of years. Man could not accept that when you take something from less than nothing you can get even more less than nothing. And to say that less than nothing multiplied by less than nothing could equal something was just nonsense. The arguments against imaginaries were even more profound. A number that represents the square root of a number less than one? Incomprehensible. Gauss said that if the units had not been given the names direct, inverse, and lateral as opposed to positive, negative, and imaginary, "people would not have gotten the impression that there was some dark mystery in these numbers." Today these topics are basic lessons taught in high school and college math class and are crucial for use in the complex mathematical operations of today.
But it's not my intention for today to summarize this somewhat complicated and monotonous book. What I want to dive into are some of the points made by mathematicians in Chapter VII, "The Illogical Development: The Predicament CIRCA 1800." Many arguments were made as to the necessity of proofs and rigor to define mathematics. The creation of a theorem could not be fully accepted by the mathematical community until it was proven for all n x n cases. To take on such a task for complicated (but many times useful) ideas could take years of painstaking and rigorous work. And it is these types of proofs that led the greatest minds of the 16th, 17th, 18th, and 19th centuries to spend most of their time debating about the validity of concepts instead of building upon them. Over four hundred years of going round and round in circles....
In the modern world, how much rigor should be put into analysis before accepting and pressing forward with an idea? Engineers work for years on end to prove and reprove concepts so that no error is made. But what is wrong with taking an idea, publishing a coherent paper to the world and accepting it as true? Once it is released to the vast realm of the internet, it must submit to the scrutiny of thousands of critics through comments and response. And the more interesting the concept, the more critique it will gain. These critiques can serve as the painstaking "proof" process without hindering the development of the technology. With the advent of open-source technology and wiki articles, this concept of reducing rigor and continuing development seems to already be taking hold. But within the scientific community, the slow and painstaking process of "proof" continues. Proprietary information from large corporations cripples this development process to an extent, but the quickest and most technology savvy of companies will soon learn that the pros of expedited technology insertion far outweigh the cons of technology abduction. Companies like Google are already pressing forward with this attitude to the delight of unfathomable monetary gains. Google is the 7th largest company in the world by market capitalization and the majority of its work is done in an open-source environment. The results of publicizing information, pressing forward with advancement, and neglecting that difficult process called proof and analysis, will serve for the betterment of corporations and in the long run, the betterment of the world.
Mathematics: The Loss of Certainty
By, Morris Kline
Not a book you should pick up for an easy read on a road trip to Disney World, but "Mathematics: The Loss of Certainty" goes through the invention of Mathematics from its roots with the Babylonians back in 3000 BC to the Greeks creation of Euclidian geometry to the quarrels and debates of its development that lasted through the 19th century and on to today. It's interesting to see how some of the most useful mathematical methods like negative numbers, the complex number system, and irrationals, were hotly debated topics for hundreds of years. Man could not accept that when you take something from less than nothing you can get even more less than nothing. And to say that less than nothing multiplied by less than nothing could equal something was just nonsense. The arguments against imaginaries were even more profound. A number that represents the square root of a number less than one? Incomprehensible. Gauss said that if the units had not been given the names direct, inverse, and lateral as opposed to positive, negative, and imaginary, "people would not have gotten the impression that there was some dark mystery in these numbers." Today these topics are basic lessons taught in high school and college math class and are crucial for use in the complex mathematical operations of today.
But it's not my intention for today to summarize this somewhat complicated and monotonous book. What I want to dive into are some of the points made by mathematicians in Chapter VII, "The Illogical Development: The Predicament CIRCA 1800." Many arguments were made as to the necessity of proofs and rigor to define mathematics. The creation of a theorem could not be fully accepted by the mathematical community until it was proven for all n x n cases. To take on such a task for complicated (but many times useful) ideas could take years of painstaking and rigorous work. And it is these types of proofs that led the greatest minds of the 16th, 17th, 18th, and 19th centuries to spend most of their time debating about the validity of concepts instead of building upon them. Over four hundred years of going round and round in circles....
In the modern world, how much rigor should be put into analysis before accepting and pressing forward with an idea? Engineers work for years on end to prove and reprove concepts so that no error is made. But what is wrong with taking an idea, publishing a coherent paper to the world and accepting it as true? Once it is released to the vast realm of the internet, it must submit to the scrutiny of thousands of critics through comments and response. And the more interesting the concept, the more critique it will gain. These critiques can serve as the painstaking "proof" process without hindering the development of the technology. With the advent of open-source technology and wiki articles, this concept of reducing rigor and continuing development seems to already be taking hold. But within the scientific community, the slow and painstaking process of "proof" continues. Proprietary information from large corporations cripples this development process to an extent, but the quickest and most technology savvy of companies will soon learn that the pros of expedited technology insertion far outweigh the cons of technology abduction. Companies like Google are already pressing forward with this attitude to the delight of unfathomable monetary gains. Google is the 7th largest company in the world by market capitalization and the majority of its work is done in an open-source environment. The results of publicizing information, pressing forward with advancement, and neglecting that difficult process called proof and analysis, will serve for the betterment of corporations and in the long run, the betterment of the world.
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