tag:blogger.com,1999:blog-49182298785644767792024-03-14T02:50:52.917-07:00The Mind of a Theorist - The BlogAn exploration of theoretical physics, for those who are not necessarily PhDs, but who don't want their physics dumbed-down.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.comBlogger83125tag:blogger.com,1999:blog-4918229878564476779.post-22744458016225925292013-03-17T07:06:00.001-07:002013-03-17T07:06:30.727-07:00No Session on the 23rd for Elementary Mathematical Methods<span class="userContent">Next Weekend we will not be having an Elementary Mathematics Session, the week after that we will. So no session on 23 March.</span>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-18843101328315893072013-03-10T23:08:00.002-07:002013-03-10T23:08:17.661-07:00Elementary Mathematics Lesson 1 HomeworkHere are some homework results from Di. Here we will call the Stop Reading and Do Something exercises SRADS.<br />
<br />
<span style="font-family: Garamond;"> SRADS #1 - A number is a representation of a quantity of something.<br />
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SRADS #2<br />
<span style="font-family: Garamond;"><div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-41q5Z2jYqws/UT10Mtbe9oI/AAAAAAAAAKk/5qYFdmCh0YQ/s1600/ElementaryLesson1.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="64" src="http://4.bp.blogspot.com/-41q5Z2jYqws/UT10Mtbe9oI/AAAAAAAAAKk/5qYFdmCh0YQ/s640/ElementaryLesson1.gif" width="640" /></a></div>
</span><span style="font-family: Courier;"> </span><br />
<span style="font-family: Courier;">SRADS #3: <span style="font-family: Garamond;"> We label them with numbers with what they represent like 3 apples or 2 squares.</span><br /></span><br /></span><br />Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com1tag:blogger.com,1999:blog-4918229878564476779.post-8762211723247041592013-03-02T07:10:00.001-08:002013-03-02T07:10:05.358-08:00Elementary Mathematical Methods CourseElementary Mathematical Methods Session 2 Tonight at 8 PM Central Time on Skype and TeamViewer 8.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-77469814487814618532013-03-01T07:55:00.001-08:002013-03-01T07:56:23.519-08:00Elementary Mathematics Course Lesson 1Di has proposed a Mathematica program to demonstrate some ideas from set theory. We worked on it together and it is now embedded in Lesson 1 at <a href="http://www.madscitech.org/elemath">www.madscitech.org/elemath</a>.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-19545161794922656142013-02-28T02:57:00.003-08:002013-02-28T02:58:23.509-08:00The Flame Challenge to Explain TimeIf you do not know about this, you can find the details here: <a href="http://www.centerforcommunicatingscience.org/the-flame-challenge-2/">http://www.centerforcommunicatingscience.org/the-flame-challenge-2/</a><br />
<br />
Here is my shot at it:<br />
<br />
Hours, minutes, seconds, years, these are some of the labels that we use to measure time. In this way time is thought of as a way to keep track of what happens. Each thing that happens is stamped with a time. This is the basis for all of science—measuring when things happen.<br />
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Whenever something happens, something else caused it. Lightning causes thunder. Hunger causes a pain in the stomach. The desire to know causes a question. In science we believe that causes happen at some time and events at a later time.<br />
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From this you can imagine that our experience passes from event to event. If we think about it long enough, we will see that we can sort the things that happen into events that have already happened—what we call the past; things that are happening right now—the present; and things that have yet to occur—the future.<br />
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We can think of each moment of time as a snapshot, with the entire universe frozen forever. What happened five minutes ago will forever exist in that moment, and we will never see it again the same way. What is happening now we will only be aware of at some future time. What happens in the future has yet to be determined. We are always moving through time, into the future, even if we seem to stand still.<br />
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Our ordering of events is not perfect, we do not fully understand the nature of time. It seems like there is never no time, but there are places where things happen so fast that time seems to stutter. It is also difficult to separate the notion of time from that of distance, particularly as you go very fast, or you think of things that are very big—like the Sun.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-43380423249475018832013-02-23T06:16:00.000-08:002013-02-23T06:16:34.312-08:00Elementary Mathematical Methods - Session 1Those people who want to register for the course, send me an email at <a href="mailto:george@madscitech.org">george@madscitech.org</a>. You may connect up with us tonight at 8 PM Central Time on Skype. Use my Skype name georgehrab. If you are not registered for the course, I will not respond.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com2tag:blogger.com,1999:blog-4918229878564476779.post-61116995803928565802013-02-17T00:30:00.003-08:002013-02-17T05:09:30.826-08:00The Conduct of the Elementary Mathematical Methods Course<span class="userContent">The conduct of the course will be like this:<br /> 1) Written material will be added each week.<br /> 2) Every Saturday at 8PM Central Time there will be a live session via Skype and TeamViewer. This session is very important. Do not ignore this. If you need to get a microphone for your computer, do so. Download Skype, it's free! So is TeamViewer 8.<br /> 3) Throughout the week discussions will be held at The Mind of a Theorist - The Blog. These are also important. I can only gauge how you are doing by examining your "homework". The discussions will be where you express issues you are having. It also gives those who understand the material a chance to test out their understanding by explaining things to others.<br /> I have several people who emailed me that they are signing up for the course. Anyone else who is interested, you have until this next Friday to sign up and read what I have put up already. You can sign up by sending email to <a href="mailto:george@madscitech.org">george@madscitech.org</a>.</span>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-48264295409597394562013-02-15T08:46:00.002-08:002013-02-15T08:46:45.324-08:00Elementary Mathematical Methods for Science CourseThe official web site will be here: <a href="http://www.madscitech.org/elemath/index.html">http://www.madscitech.org/elemath/index.html</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-67469421660740127662013-02-09T23:43:00.000-08:002013-02-09T23:43:16.825-08:00The Elementary Mathematical Methods Course is OnOK, there are now enough people interested to do this. I will need people to email me for signing up for the course. Use my email address <a href="mailto:george@madscitech.org">george@madscitech.org</a>.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-16338740765678968112013-02-08T20:00:00.000-08:002013-02-08T20:00:37.061-08:00Elementary Mathematical MethodsIf I can get a total of 10 people interested I will teach a course on Elementary Mathematical Methods for Science. This will consist of units on algebra, estimation and dimensions, geometry, trigonometry, analytic geometry, calculus, linear algebra, multivariable calculus, differential equations, and probability and statistics. Possibly other topics as well.<br />
<br />
I have 4 people interested already.<br />
<br />
Here is how the course will be conducted:<br />
<br />
1) Each Friday I will place material on a web site for the course. This will be in the form of a cdf file, a format created by Wolfram Research. Many of these documents will contain interactive material for you to play with. There will be a number of challenges: 2-3 will be done in complete detail, 1-2 will be done in less detail, 1-2 will be done in little detail, and 1-2 will have no detail.<br />
<br />
2) Discussions of the work will continue on the blog until the students are done with them. If this takes 2 months, then I know that I have done something wrong.<br />
<br />
3) Throughout the week I will monitor the blog to see what responses I get. This will determine the new material I put up on Friday of that week. I will also put up a record of the discussion formatted for the mathematics<br />
<br />
4) Upon completion of an assignment by all participants I will post a transcription of the discussion formatted in Mathematica and converted into a cdf.<br />
<br />
5) If people are interested, I will have a live session on Saturday evenings beginning at 8PM central time and going until 10 PM central time. This will be via Skype and will use TeamViewer as the desktop sharing software so that I can answer questions directly.<br />
<br />
6) If I can figure out a way to do it efficiently I will produce audio lectures keyed to the material, so you can follow along.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com4tag:blogger.com,1999:blog-4918229878564476779.post-34771673201546400322013-02-07T09:38:00.001-08:002013-02-07T09:38:44.805-08:00The Book is Out!!!Well, the book I wrote with Leonard Susskind, The Theoretical Minimum, is out and is a huge success! Thanks to all of you who have been following this! You can find the web site to support the book at <a href="http://www.madscitech.org/tm">www.madscitech.org/tm</a>. Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-79699738955047196322012-12-05T19:25:00.000-08:002012-12-05T19:25:14.660-08:00New Information Theory Post and Mathematica 9Mathematica 9 has come out and has some amazing new capabilities. I have produced a new information theory post using some of the new functions. This is at <a href="http://www.madscitech.org/information/information.html">http://www.madscitech.org/information/information.html</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-66726221952019698892012-11-25T15:12:00.001-08:002012-11-25T15:12:47.938-08:00For Those Wanting to Study on Their OwnI have a book on Lulu called "Self-Instruction and Teaching: Science Education for the New Millenium". This is all about how to learn effectively, and how to teach others. You can find it here: <a href="http://www.lulu.com/spotlight/george1053">http://www.lulu.com/spotlight/george1053</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-29912378633637009002012-11-21T04:02:00.000-08:002012-11-21T04:02:02.601-08:00Starting a new Writing ProjectI will be working on a textbook for University Physics, called University Physics with Modern Physics. I know, terribly original title. This book will be freely available as a series of downloads from the web site <a href="http://www.madscitech.org/upmp">www.madscitech.org/upmp</a> starting today. I envison this as a bunch of Mathematica-based cdfs (computational documents) and pdfs. I will also be able to put together custom textbooks to suit the needs of specific classes. These will be available at Lulu (<a href="http://www.lulu.com/">www.lulu.com</a>), and through the web site above. At this stage I am working on the structure of the contents. In general, here are the contents:<br />
<br />
<ol>
<li>Introduction to Physics</li>
<li>Mathematics</li>
<li>Mathematical Physics</li>
<li>Theoretical Physics</li>
<li>Computational Physics</li>
<li>Experimental Physics</li>
<li>Classical Physics</li>
<li>Modern Physics</li>
<li><span style="font-size: large;"><span style="font-size: large;"><span style="font-family: inherit; font-size: small;">Using Calculus to Model Motion</span></span></span></li>
<li>Introduction to Mathematica</li>
<li>Error Analysis<span style="font-family: Garamond; font-size: large;"><span style="font-family: Garamond; font-size: large;"></span></span></li>
<li>Newtonian Mechanics</li>
<li>Thermodynamics and Energy</li>
<li>Fields and Waves</li>
<li>Problems with Classical Physics</li>
<li>Einstein's Relativity</li>
<li>Quantum Physics</li>
<li>Applications of Relativity and Quantum Physics</li>
<li>Differential Equations</li>
</ol>
There is a LOT more, but this will be enough for now. :-)Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-47637708650939658872012-11-21T03:33:00.000-08:002012-11-21T03:33:34.773-08:00The Web Page for The Theoretical Minimum is Up!The web page for The Theoretical Minimum is up and you can see it at: <a href="http://www.madscitech.org/tm">www.madscitech.org/tm</a>.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-30692586559351847542012-11-08T02:55:00.000-08:002012-11-08T02:55:10.858-08:00Book UpdateThe book, <em>The Theoretical Minimum</em>, will be published by Basic Books at the end of January of 2013. There will be a companion web site: <a href="http://www.madscitech.org/tm">www.madscitech.org/tm</a>, it is not yet up! Don't go there and then tell me there is no link!Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-16142678423279726972012-11-07T15:18:00.000-08:002012-11-07T15:18:40.217-08:00New Writing on Information Theory: Some important theorems on Markov Chains, their proofs, and how to model Markov Chains in Mathematica. <a href="http://www.madscitech.org/information/information.html">http://www.madscitech.org/information/information.html</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-50120171406089952012012-10-25T16:03:00.001-07:002012-10-25T16:03:22.324-07:00New material on information theory at the MAST. This time on the nature of Markov Chains (finite). <a href="http://www.madscitech.org/information/information.html">http://www.madscitech.org/information/information.html</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-49209831962449452042012-10-15T07:19:00.000-07:002012-10-15T07:19:45.370-07:00New Information Theory Site on MASTI have formalized my notes on information theory and placed them on the MAST website. You can find tham at <a href="http://www.madscitech.org/information/information.html">http://www.madscitech.org/information/information.html</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-42614525211921646752012-09-28T13:51:00.001-07:002012-09-28T13:51:48.603-07:00More Information on the BookI just finished working over the proofs for the publsher. It is now in their hands again. The next step is the Galleys, and then back to the publisher again. The book is scheduled to be out in January 2012.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-49868295725965827762012-06-28T13:28:00.004-07:002012-06-28T13:29:55.111-07:00The Nature of Information VIn this installment I demonstrate how to determine some of the quantities we have been looking into using Mathematica 8. You can find it at this website:<br />
<br />
<a href="http://www.madscitech.org/csg/it.html">http://www.madscitech.org/csg/it.html</a><br />
<br />
under Information Theory V.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-48376801087133993492012-06-17T01:48:00.000-07:002012-06-17T01:48:05.304-07:00The Nature of Information IVIn this post I examine what coding is and introduce Shannon's First Coding Theorem and the Shannon-McMillan Theorem. See <a href="http://www.madscitech.org/csg/it.html">Information Theory IV</a>.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-48628579756135023622012-06-13T22:31:00.002-07:002012-06-13T22:32:09.968-07:00The Nature of information IIIIn this posting I explore the probability of finding strings and establish the principle that the chace of finding a given string is independent from the elements of the string. This result is called the <em>Asymptotic Equipartition Property</em>. For details go to the <a href="http://www.madscitech.org/csg/it.html">The Nature of Information III</a>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-83683642899885747662012-06-01T00:13:00.001-07:002012-06-01T00:13:24.706-07:00New place for formatted information theory.Due to the difficulty in placing the mathematical symbols into the blog, I will encapsulate the post and provide a link to the formatted version.<br />
<br />
In general these will be located at: <a href="http://www.madscitech.org/csg/it.html">http://www.madscitech.org/csg/it.html</a>.Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0tag:blogger.com,1999:blog-4918229878564476779.post-67707089378660241042012-05-22T12:42:00.000-07:002012-05-22T12:42:19.837-07:00The Nature of Information II<h2>
The Nature of Information II</h2>
<div class="Author">
George Hrabovsky</div>
<div class="Institution">
MAST</div>
<h3 class="Section">
Introduction</h3>
<div class="Text">
The previous article was concerned primary with a sequences of events that were mutually exclusive. What happens when more than one such sequence, or scheme, are combined?</div>
<h3 class="Section">
Combining Schemes—Mutually Independent Sets</h3>
<div class="Text">
Let’s say that we have two finite schemes,</div>
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<a href="http://4.bp.blogspot.com/-Z7cUXLoEGk0/T7vqgEealpI/AAAAAAAAAHA/vVWYZIP_XL8/s1600/natinfo2_1.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Z7cUXLoEGk0/T7vqgEealpI/AAAAAAAAAHA/vVWYZIP_XL8/s1600/natinfo2_1.gif" /></a></div>
<div class="Equation" style="text-align: center;">
</div>
<div class="Text">
and</div>
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<a href="http://2.bp.blogspot.com/-CpCyUS_qE1c/T7vqmrSRCyI/AAAAAAAAAHI/re1_1qxkJdA/s1600/natinfo2_2.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-CpCyUS_qE1c/T7vqmrSRCyI/AAAAAAAAAHI/re1_1qxkJdA/s1600/natinfo2_2.gif" /></a></div>
<div class="Equation" style="text-align: center;">
</div>
<div class="Text">
Say that the propbability of the joint occurence of events </div>
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<a href="http://1.bp.blogspot.com/-tVYoh4NMOiA/T7vqrEqd5VI/AAAAAAAAAHQ/QIcsWc7iD1o/s1600/natinfo2_3.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-tVYoh4NMOiA/T7vqrEqd5VI/AAAAAAAAAHQ/QIcsWc7iD1o/s1600/natinfo2_3.gif" /></a></div>
<div class="Text">
<br /></div>
<div class="Text">
and</div>
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<a href="http://3.bp.blogspot.com/-vucFcm8hZkE/T7vq0BOCftI/AAAAAAAAAHY/K_193BDvrMY/s1600/natinfo2_4.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-vucFcm8hZkE/T7vq0BOCftI/AAAAAAAAAHY/K_193BDvrMY/s1600/natinfo2_4.gif" /></a></div>
<div class="Text">
</div>
<div class="Text">
is</div>
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<a href="http://4.bp.blogspot.com/-CZn1k2zm7EI/T7vq464s88I/AAAAAAAAAHg/sfkxtbIo32Y/s1600/natinfo2_5.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-CZn1k2zm7EI/T7vq464s88I/AAAAAAAAAHg/sfkxtbIo32Y/s1600/natinfo2_5.gif" /></a></div>
<div class="Equation" style="text-align: center;">
</div>
<div class="Text">
This property is called a <span style="font-style: italic;">mutually independent probability</span>. In fact the set of events</div>
<div class="Equation" style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-9KS5k1V2E5E/T7vrB_SN4TI/AAAAAAAAAHo/2CB281jEHxc/s1600/natinfo2_6.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-9KS5k1V2E5E/T7vrB_SN4TI/AAAAAAAAAHo/2CB281jEHxc/s1600/natinfo2_6.gif" /></a></div>
<span id="goog_1184769302"></span><span id="goog_1184769303"></span></div>
<div class="Text">
forms another finite scheme. The entropy for such a scheme is,</div>
<div class="Equation" style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-vVXrmYxx8Gw/T7vrHzPfOfI/AAAAAAAAAHw/UxMbjl3vUlQ/s1600/natinfo2_7.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-vVXrmYxx8Gw/T7vrHzPfOfI/AAAAAAAAAHw/UxMbjl3vUlQ/s1600/natinfo2_7.gif" /></a></div>
</div>
<h3 class="Section">
Combining Schemes—Mutually Dependent Sets</h3>
<div class="Text">
So what if <em>A</em> and <em>B</em> are not mutually independent? Here we say that the probability of event<br />
<div class="separator" style="clear: both; text-align: center;">
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<br />
of the scheme <em>B</em> occurs assuming that event<br />
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<a href="http://1.bp.blogspot.com/-e8AUK1AcG70/T7vrWn9hWBI/AAAAAAAAAIA/BjZQJLM6-EQ/s1600/natinfo2_9.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-e8AUK1AcG70/T7vrWn9hWBI/AAAAAAAAAIA/BjZQJLM6-EQ/s1600/natinfo2_9.gif" /></a></div>
<br />
occurs from scheme <em>A</em> is</div>
<div class="Equation" style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-5U3UUu6tHOY/T7vrbn3_D5I/AAAAAAAAAII/cq0a2GOElAU/s1600/natinfo2_10.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-5U3UUu6tHOY/T7vrbn3_D5I/AAAAAAAAAII/cq0a2GOElAU/s1600/natinfo2_10.gif" /></a></div>
</div>
<div class="Text">
This gives us the scheme</div>
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with entropy</div>
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It turns out that<br />
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is a random variable called the expectation of <em>H</em><em>(</em><em>B</em><em>)</em> in the scheme <em>A</em>. It is also written<br />
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<h3 class="Section">
What does It all Mean?</h3>
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The amount of information delivered by a scheme never decreases unless a another scheme is realized beforehand.</div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/01047370759423352210noreply@blogger.com0