Paul Nervy Notes
“Jokes, poems, stories, and a lot of philosophy, psychology, and sociology.”

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Math.  ---  .This section is about mathematics.  Topics include: ( ) Applications.  ( ) Branches.  ( ) Philosophy of math.  ---  1/24/2006

Math.  ---  (1) What separates the different branches of math?  Different types of numbers?  Different types of operations?  Different types of problems they solve?  Different areas of application?  (2) What do all the branches of math have in common?  (3) What connections are there between the various branches of math?  ---  8/25/2004

Math.  ---  Applications of math.  In science math is useful for putting physical laws in mathematical format.  Physics.  Engineering.  Statistical inference in the sciences.  Statistics for public opinion polling.  Accounting for money.  ---  10/8/2005

Math.  ---  Applications of mathematics.  (1) Engineering.  (2) Accounting.  (3) Statistics.  ---  9/5/2004

Math.  ---  Applications.  Best application for your problem vs. overkill vs. underkill.  Cost of solution in money, time, energy and materials.  ---  12/30/1992

Math.  ---  Applications.  Most to least important, common, and useful applications.  ---  12/30/1992

Math.  ---  Applications.  Some important applications of math.  (1) Standardization of parts.  (2) Describe natural laws as formulas.  (3) Solve problems.  (4) Computers.  ---  12/30/1992

Math.  ---  Applications.  What areas of math are useful for what areas of life?  ---  12/30/1992

Math.  ---  Arguments against math.  Math is mechanical, algorithmic, rule-based, boring, not creative.  ---  7/14/2006

Math.  ---  Arts and math.  Music is very mathematical.  Visual arts can be mathematical.  Is literature mathematical?  Only if you number your sentences.  ---  6/5/2004

Math.  ---  Branches of mathematics.  Relationships of the branches.  Applications of any branch in subject areas (ex, business).  ---  12/30/1992

Math.  ---  Branches.  Foundations, set theory, arithmetic, algebra, trigonometry, geometry, calculus, topology, probability, combinatorics, statistics, numerical analysis.  ---  12/30/1992

Math.  ---  Branches.  Questions for each branch.  How wide and deep is the body of theory?  How wide and deep is the body of applications?  ---  12/30/1992

Math.  ---  Computers and math.  (1) How has the development of computers depended on mathematical advances?  (2) How has the recent development of mathematics depended on the computer?  How do computers aid our ability to do math?  The computer can do many large calculations quickly.  ---  6/5/2004

Math.  ---  Computers and math.  Is there any math that cannot be done on a computer?  ---  4/15/2002

Math.  ---  Computers and math.  Mathematica software.  How much has Mathematica changed academic math?  Computer posed problems and computer solved problems.  Can math be automated?  ---  12/30/2003

Math.  ---  Evolution of mathematical abilities.  (1) Mathematical abilities in animals.  (2) First mathematical concepts in humans.  "One, many (more than one)".  "One, two, many".  "One, two, three, many."  ---  6/5/2004

Math.  ---  Evolutionary math.  (1) Math behavior in animals.  (2) Math behavior in early humans (200,000 - 10,000 BC).  ---  5/16/2005

Math.  ---  Given you are in a situation, faced with a problem or challenge, when does it pay to use a quantitative method?  Which method use?  Why?  Time and cost of using, and not using, any method.  ---  12/30/1992

Math.  ---  History and origins.  How did human mathematical ability evolve?  What kind of mathematical ability do animals, such as chimpanzees and dolphins, have?  How does mathematical ability evolve in children?  ---  4/13/2001

Math.  ---  History current future.  Current state of mathematics.  (1) Measure everything, quantify everything, and keep all the data on computer databases.  (2) Data crunching.  The rise of statistical analysis done on computer, used as proof in court.  (3) Mathematical modeling, done on supercomputers, used to predict the weather, nuclear explosions, etc.  (4) Solving proofs using artificial intelligence.  (5) Andrew Weil solves Fermats last theorem.  The last solo pen and paper mathematician.  ---  4/28/1998

Math.  ---  History current future.  Who made what contribution to theory or application?  What was their work called?  ---  12/30/1992

Math.  ---  History of math by subject, geography area, and time period.  ---  12/30/1992

Math.  ---  History of math.  (1) Discovery.  Being unconscious vs. conscious (A) Of thing discovered (realizing you found something).  (B) Of knowledge that it was a new discovery.  (C) Of importance of discovery.  (2) Looked for vs. unlooked for discoveries.  (3) Expansion or refinement of existing theories.  ---  12/30/1992

Math.  ---  How important is math?  What tells us more about the world, numbers or words?  Some would argue that numbers are more important than words because the accumulation of numerical data gives us a more accurate depiction of reality than words.  Others argue that there are some things that cannot be quantified, that words capture better than numbers.  Other people argue that the most important things cannot be described by words or numbers.  Whatever they are.  ---  4/13/2001

Math.  ---  How much has math contributed toward making the world the way it is?  How much has math let us accomplish?  Where would we be without math?  What would the world be like without math in general, or any type of math?  ---  04/15/1993

Math.  ---  How much of the world, the natural world, the human world, can be modeled by math, or can be described and explained by math?  I.e. How powerful and useful is math?  What can't math do yet or ever?  ---  11/30/2003

Math.  ---  If there are six billion people on earth, and 365 days in a year, then you share your birthday with how many people?  Approximately 16 million?  ---  7/11/2001

Math.  ---  Infinity: forever.  Zero: nothingness, void.  Both are very cool mathematical concepts because neither actually exist.  They are imaginary.  ---  1/18/1999

Math.  ---  Logic and math.  Is math a form of logic?  Is logic a form of math?  If math and logic are two different things, how are they similar and different?  ---  6/5/2004

Math.  ---  Logic and math.  Reducing math to logic.  How close did Russell come to reducing math to logic?  ---  4/15/2002

Math.  ---  Math is all about measurement.  Measurement is about small equal gradations being more exact than adjectives like light and heavy, etc.  Once you can measure, it becomes all about gathering and recording a lot of data, and analyzing it for patterns.  Not a single equation need be done.  No math, just numbers.  ---  8/1/1998

Math.  ---  Math of the future.  Mathematicians will think of problems, and reasoning computers will solve them.  ---  01/06/1997

Math.  ---  Math to describe situations vs. math to solve problems.  ---  4/15/2002

Math.  ---  Mathematical knowledge.  Math is an area in which we are supposed to be positively sure of our knowledge.  True by definition.  True by logic.  ---  10/12/2006

Math.  ---  Mathematical theory vs. application (technology).  Discovery of, and organization of each.  ---  12/30/1992

Math.  ---  Number.  (1) The thing.  Number of physical objects.  Units of measurement.  Lumpy.  (2) The written symbol and the spoken word.  (3) The idea: infinity, progression, smooth.  ---  12/30/1992

Math.  ---  Our society has little patience for things that cannot be quantified with numbers, and even less patience for things that cannot be described with words.  ---  4/13/2001

Math.  ---  Philosophy of math.  (1) Metaphysics: metaphysical status of number.  Various theories.  (2) Epistemology: arguments for above metaphysical theories.  Epistemological status of mathematical proof.  ---  12/30/1992

Math.  ---  Philosophy of math.  (1) What is a number?  This question is often viewed as the main question in the philosophy of math, but the following questions are just as important.  (2) What is an operation?  (3) What does "equals" mean?  (4) What is a mathematical proof?  ---  7/12/2002

Math.  ---  Philosophy of math.  Epistemology.  Proof types: absolute mathematical proof or disproof.  ---  12/30/1992

Math.  ---  Philosophy of math.  Thing, idea, number (is just like) thing, idea, word.  ---  12/30/1992

Math.  ---  Philosophy of math.  What is a number?  Answers can vary because there are many types of numbers: whole, natural, integer, real, rational, irrational and transcendental numbers.  One possible view is number as concrete amount or quantity, for example, whole numbers and fractions.  Another view is number as abstract idea or concept, for example, negative numbers and randomly repeating numbers like pi.  ---  7/12/2002

Math.  ---  Putting a problem or data in logical or numerical form, and figuring out how to solve the problem.  ---  12/30/1992

Math.  ---  Related terms.  Math, logic and computers.  Functions, algorithms, laws, rules.  ---  4/15/2002

Math.  ---  Science and math.  Math enables science by allowing experiments to be quantified.  ---  6/5/2004

Math.  ---  Terms to be analyzed: concepts, laws, operations, and elements.  ---  12/30/1992

Math.  ---  The psychological aspects of the concepts of number and quantification are more interesting than the philosophical aspects of those same concepts.  How did mathematical ability evolve in animals and humans?  ---  1/24/2002

Math.  ---  Time and temperature are both arbitrary manmade creations.  ---  1/18/1999

Math.  ---  What are the limits of math?  Will mathematical knowledge grow endlessly or have we figured out almost all of math?  ---  4/13/2001

Math.  ---  What can be quantified?  (1) What can be counted?  Anything there is more than one of.  (2) What can be expressed in an equation or expression?  Anything that has a regular pattern.  (3) What is a regular pattern?  Anything that repeats.  Anything that humans notice repeating.  (4) Are there regular patterns that humans cannot recognize but that other animals or computers can recognize?  Yes.  (5) A statistical pattern is a type of a pattern.  (6) How does recognizing patterns help?  It helps determine cause and effect.  (7) Is math as useful in the social sciences as the hard sciences?  Are there social laws as well as natural laws?  ---  5/24/2005

Math.  ---  What can be quantified?  Anything?  What can't be quantified?  ---  10/5/1999

Math.  ---  What can't be quantified?  All the values that modern society under emphasizes, like emotions.  Our society devalues things that can't be quantified.  That is a big mistake.  ---  6/5/2004

Math.  ---  What is the difference between an operation and a function?  Operations are performed on two numbers.  Functions are performed on a single number.  ---  5/12/2005

Math.  ---  What types of math are used in today's society?  How often are they used?  How important is the use?  ---  04/15/1993

Math.  ---  What.  (1) Math is law-like.  Math is good for developing scientific laws.  (2) Math is rule-like.  Logic is rule-like.  Laws are rule-like.  ---  4/22/1999

Math.  ---  What.  (1) Notation: symbolization of idea of physical quantity.  (2) Quantity: amount.  Space (distance, size, volume), time, weight.  ---  12/30/1992

Math.  ---  What.  Math is the relationships of quantities which are symbolized or modeled by numbers.  Numbers are ideas or concepts symbolized.  ---  12/30/1992

Math.  ---  Where does math end and computing begin?  Where does math end and philosophy begin?  ---  08/24/1994

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Paul Nervy Notes. Copyright 1988-2007 by Paul Nervy.