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Voter Fraud: Type I & Type II Errors.

Caveat: IANAL, I am ignorant of the law, however, I know a little about statistics and testing hypotheses. On one hand: Suppose we are confronted with making a decision based on limited data; most real world data is incomplete. Consider, for example, the charge that Ted murdered Jack Our legal system doesn’t require that jurors be omniscient. It only requires that jurors begin by assuming that Ted is Innocent until Proven Guilty . In more precise language, jurors should begin with the hypothesis that Ted is not guilty  as opposed to the alternative that Ted is guilty . Jack is guilty is not a reasonable alternative hypothesis.  We do not test whether Ted is innocent versus Ted is not innocent . If the reason for this is not immediately obvious, I hope it soon will be. The jurors examine the presented evidence, and ideally without bias, evaluate the accumulation of evidence and arguments. If the accumulated arguments and evidence presented by the prosecution persuades the jury
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Axioms, Definitions, and Alternate Facts.

Things I don't understand: Consider freedom, a word that is a rallying cry for all kinds of actions that might suppress rather than engender freedom. What is freedom? How is it defined? If it means what you think it does, would freedom ever need a modifier like relative or absolute? Does the word mean the same thing to everyone? Robert Frost said "You have freedom when you're easy in your harness." My interpretation of what Frost means is that if the constraints of society and the limitations imposed on you by your body, beliefs, abilities, etc., do not rest too heavily on you, then you feel free. Can we demand freedom for ourselves and yet deny it to our fellows? The hand you feel lightly on your shoulder may be an intolerable burden crushing your brother or sister. If you think there is an easy answer, then you're reading the wrong post. Defining words is not always easy. If a definition is intended to inform someone, then that definition must
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Judicial Philosophy, Part 1

  Preamble Sitting members and nominees to the Supreme Court often identify themselves by a particular judicial philosophy concerning their interpretation of the Constitution or have some such label applied to them by observers. One purpose of labels is to serve as a code word to simplify the general approach that judge will use when applying the Constitution. Another use is to obscure intent, particularly when it allows the judge and her supporters to avoid answering difficult questions during the nomination process. With the enablement of the party controlling the Senate, such avoidance is practiced by nominees from both Democratic and Republican presidents. In my opinion, these labels serve little practical purpose except to alert a political base, nevertheless I will list six judicial philosophies, a perfect number that pleases me, for discussion. What are the most common of these judicial labels, and what philosophies and opposition do they suggest? First a disclaimer, (cavea
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Coronavirus: Flatten the Curve, Delay the Onset

Coronavirus: Spread Out the Cases to Flatten the Curve and Delay the Onset Some disclaimers and miscellaneous comments: I AM NOT A MEDICAL DOCTOR. None of the following should be construed as medical advice, or actual pandemic data, or risk assessment for any person or group of people. I suppose I could have used the acronym IANAMD but I don’t find that nearly as entertaining as the acronym for I Am Not A Lawyer. However, IANAD (I am not a diplomat). You may not enjoy my attempts at humor, but IMHO, even serious topics sometimes need comic relief. First, what does it mean to spread out the cases and flatten the curve? This discussion is for those folks that think “If you’re gonna get it, you’re gonna get it. Might as well get it over with.” Fatalism: No matter what we do, if some percentage, say 70%, will become infected eventually, then why should we do anything?              It’s not that simple. The news provides us with a perfect case study. Then comes the hospital
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Wealth and Taxes.

Recently, I've read a few comments, primarily from very wealthy people, about the proposed wealth tax . I haven't decided whether this is a good idea or not, and so I did some shallow investigation beyond newspaper headlines. Most of us already have a good idea about what tax  means, but wealth is not immediately obvious. I've checked several sources on what  wealth  usually means. The most common interpretation of wealth I've encountered is that it's equivalent to Net Worth . Basically, N et Worth = assets - liabilities, where assets include the value of all your cash and things you own, and liabilities consist of your obligations and the money you owe. Hence, if you bought a house for $250,000 and the house is valued at $250,000, then you have a $250,000 asset . If you took out a $200,000 mortgage to finance your purchase of the house, then you also acquired a $200,000 liability . If you also have $5000 in your bank account, then that is an asset.  If yo
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Things I Don't Understand

Some uses for Classifications, Definitions, Refining definitions, and Re-purposing words. On the one hand: Why do we drive on a parkway, and park on a driveway? Shouldn't hot water heaters be called cold water heaters? If the water is already hot, why heat it? Shouldn't there be another word that sounds like the word homonym but means something different or is spelled differently? See #3. Homonym apparently isn't precise enough to distinguish all possible cases. Therefore, we refine the concept with homophones, homographs, heteronyms, heterophones, heterographs, capitonyms . . . I'm not making these word up* . Even though I have difficulty remembering the distinctions among these more precise categories , I understand that for linguists, the ability to distinguish among various types of homonyms could be useful. For example, a capitonym changes its meaning or pronunciation when capitalized. For example furniture polish is not pronounced like Polish
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Whatever Happened to "Please Excuse My Dear Aunt Sally?"

Part of a student's difficulty with simplifying expressions is the blurry extension of real number operations beyond the dyadic operators of add and multiply in the field properties. For conciseness, an "agreed-to" order of operations must then include non-field operators (dyadic and monadic) and semi-logical operators. The field properties do not specify that multiplication comes before addition, and most certainly does not demand that exponents be done before multiplication. Indeed, radicals, division, and subtraction operations are usually defined at the elementary level in terms of conversion to their inverse operation: radicals to exponents, division to multiplication, and subtraction to addition. Indeed, any algebraic expression with mixed operators requires punctuation in the form of grouping symbols to specify the priority of operations UNLESS the writer and reader agree to an order of operations for incompletely punctuated expressions. Even the simplest mixed
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