“EMPTY” SPACE by Richard A Karlin

QUESTION (From Quora):

Grand Unified Theory: Lawrence M. Krauss says if you removed all of the particles, all of the radiation, absolutely everything from space and all that remained was nothing that nothing would weigh something. What weighs something is the aether. Is it not?


For starters, this question has an internal contradiction. One of the inherent properties which “empty” space manifests is the creation of virtual particles, both fermions and bosons. We know of no “empty” space lacking this virtual creation capability. So this question posits a form of space which is so far unknown in our universe.

It helps a whole bunch to start with correct physics. Energy has mass. (Recall that photons bend around a gravitation source, such as a black hole.) Where m is the mass of some energy E, and C is the speed of light, m = E / C^2 (the mass associated with that energy E is E divided by C squared, from Einstein’s equation). Energy can convert between potential which includes binding energy, and kinetic which includes radiation and thermal. When you have four hydrogen atoms, the combined mass is four times the hydrogen atom mass. When you squeeze those four hydrogens atoms into a helium atom, the mass stays exactly the same, but some of the binding energy converts to kinetic energy which rapidly disappears over the horizon in the form of radiation, neutrinos, and particle kinetic. The mass of that former binding energy accompanies it over the horizon. The helium which is left behind has less energy than the four hydrogens had and a corresponding lower mass.

No mass-energy conversion took place when the four hydrogen atoms were converted to one helium atom. Some energy was changed from potential (binding) to kinetic (neutrinos, thermal and radiation) and it dispersed, but the total energy was conserved and remained the same. Some mass was redistributed since it came from the dispersing energy, and it dispersed with that energy, but total mass was conserved and remained the same.

What we tend to call empty vacuum or empty space contains energy. This has been empirically determined and recorded in great detail in particle detectors, and while a chapter or two in the Theory Of Everything (TOE) would be nice, the truth is that recognizing that empty space contains energy does not require a TOE chapter.

Since this “empty” space contains energy, it has mass (same equation as above). Since it has mass, it weighs something.

The Michelson Interferometer cannot detect spatial change due to velocity contraction (fruitless search for the aether) or gravitational wave (equally fruitless search) because spatial change will affect each arm and everything in it, including light waves and standards, equally, causing self-cancellation in each affected arm independently. If change in all arms is self cancelling, there can be no change between the arms, so no interference results. Hence no LIGO or VIRGO output.

If calling the empty space “aether” turns you on, by all means so label it, but do not expect this to change the physics.

Since it is capable of particle creation and has energy and mass, empty space is not empty. Having energy, it has mass. Having mass, it weighs something. If it has all those things, particles, energy, and mass, imagining it capable of supporting waves does not seem unreasonable. It might be that “empty” space is all one needs for a universe or two.

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FROM WIKIPEDIA:    http://en.wikipedia.org/wiki/Ostracism

Ostracism (Greek: ὀστρακισμός, ostrakismos) was a procedure under the Athenian democracy in which any citizen could be expelled from the city-state of Athens for ten years. While some instances clearly expressed popular anger at the citizen, ostracism was often used preemptively. It was used as a way of neutralizing someone thought to be a threat to the state or potential tyrant.

Crucially, ostracism had no relation to the processes of justice. There was no charge or defense, and the exile was not in fact a penalty; it was simply a command from the Athenian people that one of their number be gone for ten years.

********************************************************************************Thank you Wikipedia.  I love you Wikipedia.

Voting was done by scratching on potsherds which were then counted.  The ostracized one could take his slaves, wives, mistresses, animals, possessions, and wealth, or any part of those,  with him.

I suggest this as a solution to 4 or 5 SCOTUS justices, some worthless Senators, and some worthless Representatives.


Posted in Political, Uncategorized | Leave a comment





Saturday, July 13, 2013




When you need an ER it is kind of late to worry about why there is none available.



Rape is a destructive heinous crime and needs to be so treated, no matter who this might embarrass.



Bob, I hope you read the above as sarcasm, the point being that you can get rid of a behavior problem by removing the target. Thus we remove dangerous things and breakable things from two year olds, but this is not an acceptable solution for adult problems. Thus we do not deal with rape by locking up all the women, nor with robbery by eliminating all the valuables, nor with drugs by giving them away free. That said, what exactly do you find complex??


Richard A Karlin The godhead in the Sol solar system is spread amongst the local sentients because all of the higher gods are busy elsewhere. GZ was packing heat, was in a vehicle, was in telephone contact with the local law, and was told to stay in his vehicle. TM had no vehicle, no heat, no telephone link. GZ was told to remain in his car. Instead he left his car, approached TM, and fired a contact shot into TM s heart. WOW!! Some plan!!



Florida law, Florida judge and jury. Not all Florida residents are raving redneck racists, but any one of the jurors could have hung that useless jury, so don’t expect the country to just buy into this travesty Florida.




That is the point Shawn. We get very concerned about bombs, but bombs

kill far less people than misused guns. I have no desire to wipe out

all the guns in the country. I belonged to my University’s gun club and

was invited to join the gun team. I had too many science labs to do so,

but I enjoyed competitive shooting (specifically, my favorite was prone

rifle, slow fire). I do not agree with guns like the MAC-10, the

American Eagle, the AK-47, and similar, in the general population.

These weapons are useless for hunting and for competitive shooting.

They are designed to kill lots of people.



Shawn, the NRA has one function in life: Maximize the sales and profits

of gun manufacturers. They do not give a rat’s ass about freedoms or liberties. I would like to see guns in the general population limited to hunting and competitive weapons with small to very modest magazines.

I would like to see background checks on owners, training requirements, proof of safe storage, and entry and tracking of gun, serial number, pin pattern, and striations. In short, a national database.



Shawn, I agree with a lot of what you say. Also, GZ put the bullet in TM’s heart, not the NRA. But the NRA is the major block to seeing that guns are not owned by nut cases or criminals and limiting gen pop guns to hunting and competitive weapons.



She cannot help lying because she is a republican, so lying is bred into her very being, part of her soul!! They not only lie, they have come to believe their own lies.



Richard A Karlin Good Diane – – – very good. I am in no way excusing her. If you listen to her and watch her, I think you will see that she is so far gone into delusion that she believes her lies completely. Earth has about 200 million square miles of surface. About 50 million square miles are land and about 150 million are water. What sane person could believe that this truly humungous surface could have been salted with 100’s of millions of years of artifacts to fake evolution?? The entire human population could not accomplish this. She is truly delusional and there is no way to fix her.



Wow!!  Pay them with things that steal their hard earned wages!!

It is hard to believe such cheap cheating bastards exist. You will not find me eating there – – ever!!


Roger Barr

Why would a loving god create such a thing as flesh-eating bacteria?

Dustin, Republicans may be larger than bacteria, but they are also a lot dumber.



Help these folk to help us steer to democracy and away from an oligarchy of the rich and powerful!!



ActBlue is a political non-profit dedicated to building online contribution software and giving it away to Democratic campaigns so they can concentrate on winning.


Bill Uglicoyote Davis shared a link.

Obama FBI nominee James Comey is not a Good Guy


Obama FBI Director-nominee James Comey is not a “good guy.” He was John Ashcroft’s deputy at the Bush Justice Department, and is hardly the hero some claim.


Are you suggesting that there are good guys to be found somewhere in the FBI??  For their last official murder of a person in custody (I believe the Fibbies called it “self defense”) they pumped 7 bullets into him, but then persons in custody can be very dangerous!!

P.S.  This did somewhat limit the information they could get from questioning said person.  I suspect the one to the back of his head may have been the coup de grace.



Such as by overeating, drinking, under exercising, drugs, ….  Can one expect the nation or the medical establishment to bear the burden of treating their ailments?


Asses will be asses!!  The rant did leave something out.  Many people with medical problems have been very sloppy in selecting their genetics.  You cannot expect the nation nor the medical profession to compensate for your poor choice of genetics.



Hi Gary,


I have nowhere near enough knowledge of PETA, so let me tell you what I do and do not believe. Let me also add that I have no connection with PETA.  I am not a member.  I am not a contributor. I see their name pop up from time to time.


I am opposed to humanity wiping out species for the sake of human convenience, such as to put down another road or to build a cheap dam.


I am opposed to killing all the elephants so everyone can have a carved ivory doodad, and incidentally making ivory doodad dealers very wealthy. Likewise concerning shark fins, bear organs, fur pelts, rhinoceros horns, etc.


I am opposed to clear cutting the planet for the well being of animals and incidentally the for the well being of us humans.


I am opposed to anything which creates major oil spills or similar.


I am opposed to poisoning the water and to creating significant earthquakes by such activities as deep well fracking.


Some species such as most primates, whales, and dolphins have considerable sentience, and I believe we should recognize this and treat these species accordingly.


I am opposed to causing animals physical or psychological pain by over confining them (as in small cages) or forcing them to do painful or unnatural things.


I am opposed to wiping out all the bison or all the wolves on the planet because these animals compete with humans for food or water or space. They were here before us, they are part of nature’s food chains, and once they are gone, they are gone.


I am opposed to things such as certain insecticides which wipe out things such as bees, both for the bees’ sake and for our sake because we need them to pollinate our crops and our vegetation.


I am opposed to cock fights, dog fights, bull fights, etc.


I am opposed to poisoning the food chain, such as by use of lead shot.


I believe domestic pets should be protected by such as vaccines and medicines and prevented from over breeding to where they must be put out to die or be put to death.


I am opposed to regularly feeding farm animals antibiotics because this breeds super bugs and makes our antibiotics useless for treating humans.


I am opposed to feeding food animals small doses of arsenic because this harms humans.


I am for raising food animals as humanely as possible, all things considered. I believe animal slaughter should be humane. These last three paragraphs will have a modest impact on food prices.


I think this covers it.  I hope you do not take offense at these things.  I eat most foods.  I have no problem with controlled hunting.


Thank you for your correspondence.


My email address is rakarlin@ieee.org


Best regards,


Richard Karlin





Snivel snivel, moan moan, piss piss…


Yes the Government IS the problem, but in a democracy, WE THE PEOPLE ARE THE GOVERNMENT.  We, the voters, sent these jackasses to Washington, and WE, the voters, are allowing them to sell us down the river.


We have allowed them to convert our democracy to an oligarchy of the wealthy and all the moaning and pissing does NOTHING!!


All reading this have access to a computer. How many have signed CARE2 petitions?? How many have telephoned a senator or a representative?? How many have donated $10 or even $5 or $3 to a candidate or a lobby group or the DGA or the DSCC?? The answer is damn few, and now everyone is pissed because the wrong things are happening.


If they don’t think you are paying attention, then why should they worry about what you want. All you need to do is type in  thepetitionsite.com or care2.com  and find petitions for what you support.  They will ask for a donation afterward, but that is totally voluntary.  (But keep in mind that even $5 or $3 helps and it lets them add you to the contributors count which impresses those with deeper pockets and those who sit in the government.)


Type in representative and your 9 digit zip and you will get your state and federal representatives and phone numbers. No stamp needed; no envelope needed.


Type in senator and your 5 digit zip and you will get state and federal senators and phone numbers.


NOW you have someone you can snivel, moan, piss, shout, scream…. To!!


If you want a true democracy, knock off the bitching and make it happen!!



Keystone XL is a disaster waiting. KILL it NOW!!



Laws should promote life, not death!!  Death trumps all rights!!



THE BEES POLLINATE FOR US. As go the bees, so go we!!  Let’s hear it for Bees!!



These are insane laws. In a sane state even a policeman who shot and killed an unarmed teen because he “felt threatened” would be relieved of his gun, badge, and job. This “tombstone vigilantism” must end.



If it is dangerous, it should be labeled. If it is perfect and flawless all the more reason to label it.  In short, label it.


Reji Larco

Banoosh » Peru to Provide Free Solar Power to its 2 Million Poorest Citizens » Banoosh


Yes Reji, but Peru does not have to fund the planet’s most expensive peeping tom show.




Richard A Karlin shared Real Truth Now’s photo.

It costs in prison expense. It costs in damage to families. It costs in damage to prisoners. But we have almost no crime, and hey, whose counting??



Surely long confinement to solitary classifies as “cruel and unusual punishment”.  Oh wait – -my bad. It meets the cruel part but in the USA not the unusual part!!



I believe it was Mills who said, “Your right to swing your arms stops at my nose.”  You have transgressed to a point well beyond the nose and it will cost you.  You are free to live your own set of religious values, but the cost of that freedom is that you are forbidden to impose them on the rest of us.  You have transgressed here, and it will cost you.  So to hell with you and to hell with your value set.  We will be coming for you!!



The ultimate perversion is not some sexual or gender thing; the ultimate perversion is stealing the freedom of a sentient living creature — human or nonhuman. That is the final perversion; the act of a truly sick mind. Hospitalize these sick people and free their slaves.



With the FDA to protect you, you do not need terrorists, you already have them; government sponsored and government paid terrorists.



With some effort, almost anyone can be educated beyond their intelligence.  Of course, with some people it takes very little effort.



Work for the passage of Warren’s Glass-Steagall re-enactment.



It is well past due to start treating these primates as the sentient creatures they clearly are!!!!



Your children, your grandchildren, your great grandchildren, (and their children for 100s of thousands of years) will pay dearly for the arrogant greed of a handful of bastards!!  Look and understand!!



I don’t know whether it hurts more that you guys are stupid enough to allow this or that we are the ones financing it.



It is way past time.  The whole point of a minimum wage is to assure a just minimum wage while still keeping McBurger, KingBurger, and Trendy all on a level playing field.   The minimum wage should increase every single time congress pays itself more!!


Larry Summers as Federal Reserve chair

Don’t you dare appoint this sick, dumb, incompetent misogynist to any government post, and certainly not the Federal Reserve!!



Depends on the police officers.  Russian ones??  Nazis??  I could adjust to doing without such as those!!



William Price, surely you believe in try, try, again, until you get it right.



No need to space travel to find intelligence. We have it here in the water and the jungles: Dolphins, whales, and primates.  But not so much in the cities.



Poison them young, before they can figure it out.


Larry Summers as Federal Reserve chair

Don’t appoint this sick, dumb, incompetent misogynist to any government post, and certainly not the Federal Reserve!!



They were here before us. They are part of nature’s food chains. Once they are gone, they are forever gone, Show some respect for nature and for our planet.



Primates are sentient.  Killing them should be a crime.  Killing them should end, NOW!!



I wondered where all of that arsenic was going, but who would have guessed eaten by chickens??  The question is: “Is the FDA corrupt, stupid, or otherwise incompetent??”



The shareholders and customers of a corporation have a right to know that corporation’s public actions!!



It takes two to have a rape, so the victim must have been a co-conspirator.  If you leave Dubai, you might not want to try that.  Most of the planet has a somewhat different attitude!!



Flush Rush before Rush flushes you!!



Posted in Uncategorized | Leave a comment



Squibs are short comments in response to news items or postings.


Keystone XL and Arctic drilling are both really bad (obscenely bad) ideas.  Congressmen, don’t promote really bad ideas, it will lead people to decide you are very stupid.


He was born in the USA and that makes him a citizen. Those who have a problem with this definitely have a problem, but Sebastian is not their problem. Maybe they got dropped on their heads once too often; maybe they cut too many classes. They need help.


You are a wicked man; for making life difficult for women you will surely burn in hell.


A federal appeals court recently ruled that a similar law passed in Franks’ home state was unconstitutional. These laws would ban abortion at just the time when women can get critical tests that tell them about the health of their pregnancy. Every pregnant woman faces her own unique circumstances, challenges, and potential complications, and it is every woman’s constitutional right to make her own medical decisions without interference from politicians who presume to know better.


They were here before us. They are part of our heritage.  They are part of our environment.  We should protect our heritage and our environment.

Killing things is a lot easier than creating them — especially live things.  So let’s not kill off all the life on the planet for our convenience.


I do not agree with DOMA. I do not agree with tax money being spent to defend DOMA. DOMA is a sure loser. Maybe next week, or three weeks, or 3 months, or 3 years, but it is going down the toilet. Stop spending our money defending this doomed bill.


Equality is the magic word. It is the backbone of the philosophy which built this country. We need absolute universal equality, and those who have trouble adjusting will eventually learn to adjust.


We do not elect and pay Senators to run their mouths. Unlimited debate is absurd. Eliminate it!!


There are no fixes for the hormonal balance someone was born with, so no point to exposing such persons to the ministrations of idiots. Respect each person’s gender and gender preferences.

You should not be subject to moronic inanities just because your inherent biology has made you different, no matter what these differences are.


It comes down to Monsanto or most of the rest of us, so let us make bye-bye Monsanto!!


For the rest of my life, I will do everything in my power to oppose the reelection of the 45 senators who abandoned the American people.

We need gun control.  This lawless licentiousness disguised as “a civil liberty” must cease.  If our current legislators cannot support gun control, we will find some who can.


The time has come to disband the NRA, bar it from our country, and put its leadership on trial for domestic terrorism.  The goal of this terrorist organization is to sell arms of all types to all manner of people without limit or qualification and without regard to the safety of USA citizens.

The 9/11 attack caused 3000 deaths.  The Oklahoma bombing caused 168 deaths.  Guns cause over 10,000 homicides per year; over 100,000 homicides per decade. You are just as dead whether killed by the explosion of 1 small gun cartridge or by the explosion of a multi-ton bomb. We have had enough!!

The NRA bribes congress to suppress any control over guns. These are acts of terrorism. The only principle involved here is profit. To HADES with the NRA and to GITMO with their terrorist leadership. Disband these terrorists, ban them from the USA, and jail their terrorist leadership.

100,000 Homicides per decade; 200,000 shooting deaths per decade. It does help keep the population down!!

100,000 homicides per decade from guns. 200,000 deaths per decade, from guns.  Death trumps all liberties and rights.


Will someone tell this somewhat earlier immigrant to treat current immigrants with more respect?!


Read this carefully, but do not weep, because weeping will do no good; scream like hell, shout and yell, jump and flail about!! Speak out!! Do not go quietly!!

If you really want a democracy, then every so often, you must stand up to scream and shout and to be counted!!

Law and justice without compassion are only another form of tyranny!!

Pay attention here please, because your government is getting very close to my “I AM TOTALLY PISSED OFF” POINT.

This is an obscenity.  This cannot stand. This must not stand. Fix this absurdity!!


Something is very wrong with a society which must jail so very many people!!


Insure the “sapiens” in “homo sapiens”!!  Strip away all education (which includes culture) and you have a primate but not a homo sapiens.  Strip away most education and you have, at best, a cruel mockery of a homo sapiens.


Keystone XL is an amazingly bad idea.  If there were a Bad Idea Nobel, it would be a real shoo-in.


It is beginning to seem that the “terrorists” are the folk in charge of the NSA.

What ever happened to peeping in the windows of apartments and parked cars??  These peeping people have a disease, and it may not even be treatable.

I urge the government in the strongest terms to do nothing to interfere with the travels or political asylum process of Edward Snowden. The U.S. government must not engage in abduction or any other form of foul play against Mr. Snowden.  Secrecy laws do not allow the government to use them to abuse its own citizens.

Mr. Snowden, thank you for your courageous act.


You are a VCU student, a Cucci supporter, therefore a republican, therefore a “know-nothing”, a climate denier, an Obama-hater, and an equality denier; and YOU want to discuss maturity?? Must we accept earth-centric, flat-world, and air in outer space (because god abhors a vacuum) beliefs to discuss maturity with you Chris?? Cucci is too dumb to understand why 90+% of the scientific community of the world believes there is a climate change problem. Cucci is too stupid to understand that the only reason asses like him have personal freedom is that others are forbidden from imposing their personal views on Cucci. What is your excuse??


There is nothing patriotic about unconstitutional law!!


Gods and their trappings are created by people fearful of the seeming randomness of the universe and the awesomeness of its power, or by people trying to explain why existence exists.  The history of mankind is blanketed by dead gods, because the first of these does not work, (prayer to the gods does not affect the behavior of the universe), and the second is impossible as you cannot explain existence from within existence!!  In proof of this, consider that ‘existence IS’ because you exist.  But this is a tautology, not a proof.  You cannot construct a proof (a reason) because you keep getting the tautology!!


These long-term vacancies are an insult. You cannot compromise with great white sharks or Republicans as neither has the mental capacity to understand compromise. Call them out.


The thing about making war on your constituents and fellow citizens is that we get to shoot back.  Lock and load, Governor.


NO.  NO.  NO.  If it comes up 3700 times, my position is still NO.  I invite you to get with your constituents and support their needs.

If Obamacare is such a terrible thing, why in hell are we paying for your (CONGRESS’S) health care??  In fact, since we are getting no complete health care package, no student loan fix, no immigration repair, no tax overhaul, no climate change fix, no GE food labeling,  … , why the hell are we paying you guys anything at all.


This is as stupid as that bunch in Japan who somehow failed to learn that a generator site must ALWAYS have electricity, especially a nuclear one.

SCOTUS AS A CURE (for anything)

At its best, SCOTUS is a crapshoot.  Pissing on the voters who elected you to your state legislature is not going to help your career.  You were elected to represent the voters, not a collection of fanatics, and the voters favor choice.  If you cannot do the job, there are always more people ready to run for state office.

Justice Scalia is the very essence of bigotry.

These five ass-wipes (referring to the Voters Rights gutters) represent only themselves.


Finally, we get a sane SCOTUS decision. Maybe the drugs have worn off. There are people who would patent water molecules and oxygen molecules if they could. A sane society must apply checks to avaricious behavior.


The ultimate perversion is not some unconventional sexual thing, nor is it some unconventional choice of who you choose to live with or experience life with; the ultimate perversion is stealing the freedom of a sentient living creature — human or other. That is the final perversion; the act of a truly sick mind. Hospitalize the sick. Free their slaves.


Accepting someone’s working hours and paying them less than a living wage is a fraud upon society, upon the country, and upon humanity. This charge against Walmart (and many others) is true and its truth is a disgrace upon us. This amounts to theft, robbery, stealing, cheating, … , and it is totally unacceptable!!


You folk are either insane or you are working for the evil one; I cannot tell which. If you have a mental problem please get some help.  If you are working for the evil one, shame on you.


Franchise fairness is the bedrock of democracy.  This is not Hitler’s Germany nor is it Stalin’s Russia. Democracy requires fairness in state districting and in voting regulations. If necessary, our democracy can live without SCOTUS, but not without election franchise fairness.  In a real democracy, the right to vote is fundamental, not peripheral.


Let’s review: We had prohibition, but that did not work too well. The war on Iraq, but that left something to be desired. The war on drugs, but I am pretty sure we are losing that. The war in Afghanistan, but that is at best a draw. Now the Republicans are ready for a war on women (our own women, not someone else’s women). I think it is time for a war on Republicans.

Posted in Cultural, Economic, Political, Scientific, Social | Leave a comment


by Richard A Karlin


Achilles and the Tortoise


Zeno of Elea was born circa 490 BC of Greek heritage.  He lived in southern Italy, and he was a Pre-Socratic philosopher of the Eleatic school.  Zeno developed a series of “paradoxes” now known as Zeno’s paradoxes.  He died circa 430 BC.


These so-called “paradoxes” were in support of an argument which only a bevy of philosophers in their cups could appreciate.  Mostly I leave it to the reader to research the initiating dispute, but in short, the argument had to do with the nature of motion: 1) Real or unreal; 2) Continuous or Discontinuous.


“Zeno’s paradoxes” are not really paradoxes, but rather they arise from improper data recording technique, and the error should be crystal clear to any modern physicist.


Let us examine one of the most famous:  Achilles, the warrior and Torty, the Tortoise run a foot race.   You can set it up in an infinite number of ways, but essentially Achilles is much faster (we will use 10 times faster) and the race can be any length (we will use 1.250 mile).   Achilles being much faster, we give Torty the tortoise a one mile head start.


So Achilles has 1.250 miles to run at a speed of 10, and the tortoise has 0.250 miles to run at a speed of 1.  We are comparing the two so absolute speed in not relevant.  Achilles will run the race in a time of 0.125, and Torty in a time of 0.250.  Achilles wins; end of story.


But Zeno argues that while Achilles runs the one mile lead, the tortoise runs 0.1 mile, and when Achilles runs the 0.1 mile, the tortoise runs 0.01 mile, then respectively they run in 0.01 and 0.001, then 0.001 and 0.0001, and so on ad infinitum.


Understand please that the race is analog (as opposed to digital) and continuous – neither man nor beast stops.


Zeno has used a sample data system to record an analog race.  Now there is nothing wrong with sample data systems.  Some fabulous modern instruments use sample data.  Movies and TV are sample data systems, converting continuous views into a succession of frames.  There are some high speed oscilloscopes that use sample data.  But Zeno has sampled at ever closer intervals: the start (time zero), 0.1 time unit, 0.11 time units, 0.111 time units, 0.1111, 0.11111, ad infinitum, summing to 0.1111111… = 1/9 time units.  (The three dots is a mathematical convention meaning the digits go on forever!!)  But Achilles requires 0.1250 time units to cross the finish line; Distance 1.250, speed 10; 1.250/10 = 0.1250.  The sampling never gets to the end of the race.  Sampling is normally done at a fixed repetitive interval.  A better system might sample every 0.001 time unit.

You have put some money on Achilles in the Kentucky Derby (Achilles the horse, not Achilles the warrior).  You elect to watch the Derby on channel 99 which instead of 30 frames per second is going the Zeno way:  a frame at the start, then at 1 second, 0.1 second, 0.01 second, 0.001 second, 0.0001 second, and so one, to infinity (it will be a really long race).  Each frame is broadcast for a few seconds.  For the first few seconds all seems well.  Then the race gets slower and slower (your TV is receiving 30 frames per second no matter what the channel’s recording rate may be).  Channel 99, the “Voice of Zeno” never gets past 1.11111111… into the race, which sums to 10/9 of a mile.  Since the race is 1.250 miles long, you never get to see the finish.  Your friend is watching on ESPN which is using conventional video technology, and sees Achilles sail to a win at the 1.250 mile finish line.


No paradox whatsoever; just a faulty data recording scheme.


We can understand why a boatload of philosophers can’t parse the difference between a true paradox and a faulty data gathering scheme, and we excuse them.


It is a lot harder to understand why a modern mathematician cannot understand this difference.


It is totally incomprehensible that a modern physicist should not be able to fully understand this difference.


Sample data systems have another problem, not occurring here.  They can get tricked by something occurring at or close to the sample rate, or a multiple thereof.  The name for this is aliasing, and one example we have probably all seen is the wheels of a coach or car or train appear to be turning backwards in the movies or on video.


Perhaps in the future we can refer to “Zeno’s Disastrous Data Design”, and hopefully, hear no more nonsense about paradoxes.


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by Richard A Karlin



This is NOT a math course.  It is too compact and terse and has no practice problems.  You get good at math by doing a lot of math.  This is a review of the math that a discrete component analog circuit designer must know.  If there are holes in your knowledge, look for courses.  The Schaum outline series is very good, and it provides hundreds of practice problems.   There are many good textbooks available.

Pure versus Applied

Circuit design requires the use of applied mathematics.  You will need applied mathematics for computing component values, finding tolerances, solving circuit meshes, etc.  The areas of math required include some basic geometry, algebra, some basic trigonometry, and some basic calculus.  What is excluded is pure mathematics itself, such as constructing proofs.  Proofs such as showing that equal side-angle-side means two triangles are congruent, or proving that the square root of 2 is irrational (meaning the digits go on forever).  These are areas of pure mathematics and we only need applied math.

The metric system, known internationally as SI (from the French Systeme International) is universal in all things scientific.  A French team devised it under King Louis XVI.  It was completed and accepted under the new French revolutionary government.  Wikipedia has excellent articles on Metric / SI.

Our Base Ten Number System

Our number system is base ten.  This means that in a multi-digit number, each position from right-to-left is worth ten times the previous position.  So we write seventy-six as 76, seven-hundred-sixty-five as 765, and seven-thousand-six-hundred-fifty-three as 7653.  Seventy-six and fifty-three-one-hundredths would be 76,53.

I am using the comma as a decimal point.  This is typical European and SI usage and distinguishes decimals from sentence-stop periods.  Also, the comma is less likely to get lost than a period.  The period is often only a single pixel and disappears rather easily.  Now to make a decimal number such as 76,53 ten times larger, we need only move the decimal point once to the right: 765,3.  Remember, I am using the comma as the decimal point.  We now have seven-hundred-sixty-five and three-tenths, and we can make a shift like this with no math, no calculator or computer.  In a 10-base math system, to multiply or divide by ten (or 100, or 1000, or any number that is 10 to an integer exponent), you just move the decimal point.  This makes a standards system that is ten based very desirable.  If the kings foot had been a little shorter, or his hand a little bigger, we might have had ten inches to the foot.  This would make conversions from inches to feet (or feet to inches) a no-brainer.

The Mish-Mash System

Unfortunately, we inherited a mish-mash system.  There is some perversity in the British that made them use every base possible.  The chart of base usage below is not complete, but it gives the idea.

BASE                     USES

2—pints to the quart OR tablespoons to the ounce OR cubits to a yard

3—feet to the yard OR teaspoons to the tablespoon OR hands to the foot OR inches to a palm OR miles to the league

4—quarts to the gallon OR inches to the hand OR palms to a foot OR spans to a yard

5—fifths to the gallon (I am not sure who created the fifth, it might be French orUSA)

6—teaspoons to the ounce OR feet to a fathom

7—(I suspect they used it; I just have not found it yet.)

8—furlongs to the mile OR fingers to a yard

9—inches to the span

10—chains to the furlong

11—(I suspect they used it; I just have not found it yet.)

12—pence to the shilling OR inches to the foot

13—(I suspect they used it; I just have not found it yet.)

14—pounds to the stone

15—fathoms to the shackle

16—ounces to the pound OR nails to a yard

18—inches to a cubit

20—shillings to the pound

22—yards to a chain

32—ounces to the quart

36—inches to the yard

37—inches to the cloth-yard

1760—yards to the mile

5280—feet to the mile

The mile is actually not British.  It was one-thousand double paces (a left, then a right) for a Roman soldier.  The Roman men were a little shorter than the modern male, so their pace was a little shorter.  Mile comes from the French mil for thousand.   The famous mile stones along Roman roads were placed every thousand double paces.

If a base does not appear above, do not assume that it was not used; rather my minimal research simply did not uncover it.

Mish-Mash Distance (Length) Units


Metric Distance (Length) Units

The metric system uses exactly one distance (length) measure: the METER.

Mish-Mash Conversions

There were many more mish-mash measures in use, but those above should make the point.  Conversions within the above mish-mash are going to need paper and pencil or calculator.  Linear conversions are simplest.  If a lot is 50 feet long, it is 50/3 = 16.67 yards long.  Area conversions can require multiplying or dividing twice.  A square yard converts to 3 x 3 = 9 square feet.  A square mile contains 5280 x 5280 = 27 878 400 square feet.  I am using spaces instead of commas, every three numerals, both directions from the decimal.  This is recommended for SI usage, and it works very well.  Converting linear dimensions for a volume conversion requires cubing the conversion factor.  For example, a cubic yard (a volume one yard wide by one yard deep by one yard high) contains 3 x 3 x 3 = 27 cubic feet (a cubic foot is a volume one foot wide by one foot deep by one foot high).  Converting 100 cubic feet to cubic yards requires dividing by 3 x 3 x 3 = 27 to get 3,704 (rounded).  (Once again, that comma is a decimal.)


The Metric System (SI)

Metric System Goals

The goals of the metric system (known internationally as SI) were to reduce the number of measuring units, and to extend those units with a system of 10 based (powers of ten) prefixes.  It was a further goal to tie the units to the earth and relate them to each other.  One more goal was to standardize, hopefully all of earth.  They mostly succeeded.  Where they failed has become unimportant in modern usage.

SI Base Units

The metric system has seven SI base units:

the meter, m for distance,

the kilogram, kg for mass, and also for weight

the second, s for time,

the ampere, A for electric current,

the kelvin, K for temperature,

the mole, mol for amount of a substance, and

the candela, cd for intensity of light.

The letters following each base name are NOT abbreviations.  They are symbols, each for its unit.  They remain exactly the same for all languages and all quantities.  Thus, the symbol for amperes is A for one ampere or for 1000 amperes, and it remains the same in English, French, Cyrillic, Japanese, Chinese, Korean, Arabic, etc, etc.  It is capitalized, because it comes from the name of a scientist. The symbol for the meter is m and because it is not from a scientist’s name it is lowercase (always lower case).  The word may change in different languages, meter—metre, etc., but the symbol remains m.

SI Derived Units

The metric system currently has 22 SI derived units:

the radian, rad for angles,

the steradian, sr for solid angles,

the newton, N for force,

the pascal, Pa for pressure,

the joule, J for energy,

the watt, W for power,

the degree Celsius, °C for everyday temperatures,

the coulomb, C for electrical charge,

the volt, V for electrical potential,

the farad, F for electrical capacitance,

the ohm, Ω for electrical resistance,

the siemens, S (formerly the mho—ohm spelled backward) for electrical conductance (the reciprocal of the ohm); the final s of siemens is part of the scientist’s name, not a plural,

the weber, Wb for magnetic flux,

the tesla, T for magnetic flux density,

the henry, H for electrical inductance,

the lumen, lm for light flux,

the lux, lx for illuminance,

the hertz, Hz for the frequency of regular events,

the becquerel, Bq for rate of radioactivity, and other random events,

the gray, Gy and the sievert, Sv for radiation dose, and

the katal, kat for biological catalytic activity.

The following units are permitted:

For measuring angles:  degree (°), arcminute (‘), and arcsecond (“),

For everyday time:  minute (min), hour (h), day (d), and year (yr),

For volume and large mass:  liter (l) and tonne (t),

For logarithmic units:  bel (B), decibel (dB), and neper (Np),

For scientific use:  atomic mass unit (u) and electronvolt (eV).

The total number of units may seem large, but this covers all of daily life, commerce, production, civil engineering, and science.

Each and every one of these units can be prefixed with a prefix from the list below (which is not complete because the smallest and largest prefixes are of interest only to particle physicists and astronomers) to create a vast range of sizes.  There are currently 20 prefixes on the complete list.  Thirteen are listed below.



NAME SYMBOL   SCALE                           DECIMAL                1 BECOMES:

tera      T          Trillion times larger                    Magic Number 12        1 000 000  000 000

giga      G         Billion times larger                     Magic Number 9          1 000 000 000

mega  M           Million times larger                    Magic Number 6          1 000 000

kilo       K         Thousand times larger               Magic Number 3          1 000

hecto  H           Hundred times larger                 Magic Number 2          100

deka     Da       Ten times larger                        Magic Number 1           10

no prefix           Unit itself                                   Magic Number 0            1

NAME SYMBOL   SCALE                           DECIMAL                1 BECOMES:

deci      d          Ten times smaller                  Magic Number -1         0,100

centi     c          Hundred times smaller          Magic Number -2         0,010

milli      m         Thousand times smaller        Magic Number -3         0,001

micro    µ or u   Million times smaller             Magic Number -6         0,000 001

nano     n          Billion times smaller              Magic Number -9         0,000 000 001

pico      p          Trillion times smaller             Magic Number -12       0,000 000 000 001

femto    f           Quadrillion times smaller      Magic number -15        0,000 000 000 000 001


The Prefix Table Discussed

Let us have some important discussion about the prefix table.  The table uses the comma (,) as the decimal (.) point.  This is very SI.  I have done a couple non-SI things to it which I strongly recommend.  I have capitalized the K for kilo, the H for Hecto, and the D of the Da for deka.  I recommend capitals for prefixes greater than 1 and lower case for prefixes less than 1.  All less than 1 prefixes are already officially lower case.  To achieve my goal, kilo, hector, and deka need to shift to upper case.  (I think the SI committee will eventually come to this, but they tend to be a little bit slow.)  This will help your brain and your readers’ brains.  Brains need all the help you can give them.  Hecto, deka and deci are hardly ever used in engineering or science.  Scientists tend to use 10-to-the-power-of an integer exponents.  Engineers prefer 10 to an exponent which is a multiple of 3: Kilo, Mega, milli, micro, etc.  The Da for Deka turns a one letter prefix system into a mixed one and two letter system.  This is very stupid.  The answer is, don’t use deka.  (Alternately, D for Deka and d for deci.  It seems to work for Mega and milli.)  There are 26 letters in the Latin alphabet, yet somehow, the designers, managed to use m three times.  The SI committee has fixed this by using M for mega, m for milli, and the greek letter µ (mu) for micro.  You can get a greek mu (µ) with alt code 230 (for Windows), but this is a pain.  The engineering and scientific communities have fixed this by using u (which is close enough if you don’t suffer from OCD; of course, if you are truly nit-picky, the mu [µ] has a tail and the [u] does not, but if you have human friends, consider that they are tail-less).  The SI committee would do well to formalize this as an acceptable alternate.  The medical community has fixed this by using mc, a two letter prefix, for micro.  This is a regrettable error, and I hope they fix it.


Meter, Millimeter, Centimeter

An exception to the rule of 10-to-an-exponent-which-is-a-multiple-of-3 is centi.  For many everyday and lab length measurements, the meter is too large (a meter stick is about 40 inches—10% larger than a yard stick.  See a yardstick in your closed eyes.  Now next to it, a meter stick just 3.6 inches taller.  For most purposes, you can consider the meter to be 10% larger than the yard.  You can consider the yard to be 9% smaller than the meter.  Now you own the meter—it is yours forever.)  The millimeter, one thousandth of a meter, is the thickness of about 5-8 sheets of 20# bond paper.  The millimeter (mm) is too small a unit for most everyday and lab measurements.  The centimeter is the thickness of a thin finger (thickness, not width which is larger!).  This is a really dandy unit for around house or lab.  There are 30.5 (rounded) centimeters to the foot.  The centimeter (cm) is to metric what the inch is to the foot-pound-etc system.  There are 2.54 centimeters to the inch.  The centimeter will never go away.


Use the Prefix to Track the Decimal

The whole purpose of the prefix is to let us keep track of the decimal point.  Let us say something is 0,000 001 meter thick.  We can write this as we just have.  What about 0,000 000 000 001 meter thick.  Counting zeros now, are we?  Well, there is always 10 to some power.  For the first one, 10-6 meter and for the second one   10-12meter.  It works, but it takes a lot of key and/or mouse stroking.  How about, we use 1 micrometer thick for the first one, and 1 picometer thick for the second one.  A small capacitor used in electronics can be expressed as 0,000 000 000 010 farad or 10 picofarad.  Which of the foregoing two works better for you?  What the prefix is doing is keeping track of the decimal for you.  It also gives you a feel that the number alone misses.  I confess that 0,000 000 000 010 farad does not do it for me.  10 picofarad resonates.  The image of the part instantly springs up in my head.


SI is Cool

Note again the use of spaces between 1000 groups and comma for decimal point, and no plurals, no matter how many there are.  It is cool to be very SI.  (I will slip many times because I learned electronics long before most of the SI rules came about.  Retraining the brain is a drag, so learn SI from the start.)


The Prefix Magic Number

This takes us to the Prefix Magic Number.  If you use a prefix to change the size of the unit, like meter changing to millimeter, since the unit got much smaller, the same measurement will have to yield a larger number.  So we have something which is 1 meter long, and we want to go to millimeters.  But it takes 1000 millimeters to cover the length of 1 meter.  So we need to move the decimal point 3 places taking 1,0 to 1000,0.  Size of unit goes down, number of units goes up.  Size of unit goes up, number of units goes down.  You can do a bunch of thinking about it, or you can just learn that little mantra and apply it.  I recommend the mantra.  It leaves the brain free for other, more important thinking.

Memorize the magic numbers along with the name and symbol.  The magic number tells you how far the decimal moves.  Meter has a magic number of 0 and milli is -3.  The decimal must move three places, and since milli is smaller, number must get bigger, so move the decimal three places to the right and 1 becomes 1000.  Remember our capacitor?  It was 0.000 000 000 010 farad.  If we restate it in picofarad, pico has a magic number of -12, so it becomes 10 picofarad.  Suppose we have a capacitor that is 100 millifarad, and we wish to restate it as farad.  Bigger unit, smaller number.  Milli is -3 and farad (no prefix) is 0, so we move three decimals smaller (left) and get 0,1 farad.  Note that there are no plurals in measurements.  10 picofarad, NOT 10 picofarads.  So now we have 0,001 millimeter and want to get a whole number (1 or larger).  We need to move the decimal 3 places, and we are coming from milli which is -3.  If we go to micro which is -6, we get a difference of 3 and we are going to a smaller unit, so we will get a larger number. 0,001 millimeter becomes 1,0 micrometer, a three position shift.


Relating SI Distance to the Earth

The meter was originally supposed to be one-ten-millionth of the distance from the North Pole to the Equator along the meridian that passes throughParis.  Limits of the then technology made a truly accurate survey of this distance impossible, but they got pretty close.  Around the equator, the earth is 40 075 kilometer, so one-quarter would be 10 019 kilometer.  Around the poles, it is a little less because spin makes the earth a little bit apple shaped.  But their number was very respectable.  The standard was a bar of platinum-iridium engraved with two lines, 1 meter apart.  The meter standard today is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.  We have advanced.


Related Units: Volume, Distance, Mass

Volume is really not a separate unit, because it is a container of a certain size as measured with the meter.  For convenience, a container 1,0 decimeter on each side, which works out to be 10 by 10 by 10 centimeters, thus 1000 cubic centimeters, (symbol cc,) is called a liter (symbol L).  The liter is just a little larger than the quart: 5,7% larger.  For purchasing and storing purposes, a liter is a quart, a quart is a liter.  You now own the liter—it is yours.  SEE!!  In no time at all, you have come to really know the liter and the meter.  Who said metric was hard??

The milliliter (ml) and the cubic centimeter (cc) should be identical.  In fact, there is a standards error of 3 parts in 100,000.  I wouldn’t sweat it.  Pretty much, only standards people themselves work to 3 parts in 100,000.  (Well, plus a few physicists and a few astronomers, but not us circuit types.)  Part of the tying together of units was tying the volume to the linear, and part was that a cc or a ml of water weighs 1 gram.  This is handy.


The kilogram was defined to be the mass of one liter (1000 cc) of water at (initially 0°C—0 degrees Celsius), revised for practical reasons, to water at 4°C (4 degrees Celsius, which is where water has its greatest specific density).  Today, the kilogram is equal to the mass of the international prototype of the kilogram.  It is a physical standard, presumable platinum-iridium.  The kilogram is bigger than a pound: 2,2 times bigger.  So close your eyes, and on a two pan scale see 1 kilogram on the left pan and 2,2 pounds on the right pan.  It balances.  You now own the kilogram.  Double plus 10% gets you pounds.  For many uses, just 2-to-1 works.


The Second

Initially, the second was defined as a fraction of the mean solar day.  Fortunately for us, the earth rotates pretty regularly, but it was not quite regular enough, so a new definition was based on atomic behavior.  Now, the second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.


An SI Caution

Do remember that micro in medical use is mc, at least for now.


SI Road Distances

For longer distances, SI uses the kilometer (symbol Km).  It stays with the kilometer for all road distances.  1 Km equals 0,621 37 mile, or rounding 0,62 mile.  Going the other way, 1 mile converts to 1,61 Km.  If you use 0,6 and 1,6 for conversions, the error is only a few percent.



Problems in the Math World

Some of what we call math is really just shorthand notation.  Let us start with the real numbers.  This includes whole numbers, rational numbers (whole number fractions such as 5/6  9/10  112/254 etc.  Anything that can be written as a ratio of integers), decimals (including irrationals – numbers which never end, such as Pi, the square root of 2……), both positives and negatives of all types, and zero.  You may be surprised to learn that the introduction of negative numbers and of zero were both extremely controversial, with the best minds then around protesting both.  How, they shouted and screamed, could you have negative apples?  How could you have zero anything?  How could these brilliant men get so confused?  In part they were worrying about formal theorems and proofs.  In the applied world, if I am giving a luncheon for 20 persons, and I want each to get an apple, and there are 17 apples in the pantry, I am short three apples.  I understand minus 3 apples (-3 apples!).  If I go to My clean socks drawer, and it is empty, I understand zero pairs of clean socks!  Yet all these famous brilliant minds were terminally confused!!  A flip answer is that it is easy to educate someone beyond their intelligence, so try to bring your IQ up as you become more educated!!  In the applied world, if it gives us useful answers, it rocks.  Applied math begins with counting: |||||  |||||  ||||| .  One can optionally diagonally cross every fifth one.  Next is learning to represent the count with symbols.  5  5  5.  Next we go to a decimal representation:  15.  A larger one:  1 234,567 8.  I am still using a comma as the decimal point and a space to separate the numbers into three digit groups.  The first math operation is addition:                     12,34  +  34,63  =  46,97.

The second math operation (arguably) is sign change.  46,97 becomes -46,97 and -46,97 becomes 46,97.  The third math operation (arguably) is subtraction, but one can eliminate subtraction by using a sign change for the second number and then addition.  (One can argue that there is a zeroth math operation: counting. See!! Zero is good for some things.)


Math or Shorthand

Next is multiplication, but is it a new operation, or just a shorthand.  Let us do the product 47,97 x 23,12:



            + 47,97

            + 47,97

            + 47,97

            +  4,797

            +  0,4797

            +  0,4797


      = 1 109,066 4

So is it a new operation, multiplication, or is A X B shorthand for add A to itself B times??


De We Care Which It Is??

If we are doing applied math, do we really care which it is??  Punch it into a scientific calculator and out comes the answer.  Of course, knowing how to set the problem up, how to punch it into the calculator and how to interpret and verify the answer are all important!  As we move forward, we will see a lot more of what is (arguably) shorthand, and we do not want to be frightened or confused by something which for us is only shorthand.  Remember that no one is asking us (or looking to us) to verify mathematics.  We are just a user of mathematics.


The Factorial—More Shorthand

Another famous shorthand is the factorial, written X!, for X factorial.  The factorial (symbol !) is shorthand for the product of all integers from 1 to the factorial number.  So 3! = 1 x 2 x 3 = 6.    4! = 1 x 2 x 3 x 4 = 24.    Why start at 1? Well, if you start at 0 all factorials = 0.  Not useful.  What use is the factorial??  Probability theory.  You have five cards:  star, diamond, spade, club, heart.  How many ways can you arrange the five in an in-line order. (Only order changes).  You have five choices for the first position, four for the second, three for the third, two for the fourth, and only one for the fifth and last.  Total is 5! (5 x 4 x 3 x 2 x 1 = 1 x 2 x 3 x 4 x 5 = 5!).  5! = 120, so there are 120 ways to arrange your hand.  Unfortunately, all 120 hands rank exactly the same.  The number of different (different by cards held, not by card order!) seven card hands you can be dealt from a 52 card standard deck is 52! / (45! X 7!) = 133 784 560 (rounded).  Some of these hands will have equal rank.


Different Fields—Different Displays

In engineering practice the answer above, 133 million, would get written as 133 x 106 .  This requires several mouse or keyboard visits to format and is a pain.  An alternative is 133 x 10 exp 6.  10 exp 6 signifies 10 to the power 6.  Another option is 10^6.  The caret is upper-case 6 on the standard QWERTY keyboard.  It appears just to the right of the base (follows the base) and is followed by the exponent.  Thus one-million can be written 10^6.  Any of these will work, but metric does this with a prefix.  Our unit here is a seven-card-hand.  (A derived unit; clearly not an SI base unit!  Perhaps we can invent the symbol 7ch for seven-card-hand.)  Our answer in SI terms is then 133 M7ch, or 133 mega seven-card-hand.  NOTE:  Capital M for the mega symbol (to diff it from milli or micro) and no plural s.


Exponent (Power) Shorthand

The power superscript (example: 6 ) or its equivalents exp 6, or ^6 is another shorthand.  Just as 2 X 3 means add 2 three times, 23 means multiply 2 three times ( 2 x 2 x 2 ).  In this case, we get 8.  The number to be multiplied (2 in the last example, 10 in the paragraph above) is called the base.  The number of times to multiply the base and other important details are controlled by the superscript, called the exponent or power.  So 103 has a base of 10 and an exponent of 3.  In this case, the base and exponent are both real positive integers, but this is not a restriction as we shall see.  We can also write this as 10 exp 3 or as 10^3.  We can pronounce this as base 10 raised to power 3, base 10 raised to exponent 3, 10 to the third power, 10 to the third, or 10 cubed.  10^2 is often referred to as 10-squared, because the linear measure ten has been used to define a 10 by 10 square area, and 10^3 is called 10-cubed because the linear measure 10 has become a 10 by 10 by 10 cubic volume.  There are other variations.  English, she is a very flexible language; yes??  The important point here is that 103 is shorthand for 10 x 10 x 10.  This should in no way puzzle us or cause us fear.


Stuff about Bases

Further, BASE1, which can also be written as BASE exp 1, or BASE^1 equals BASE, for any BASE.  A mathematician would refer to this as an IDENTITYBASE0 also written as BASE exp 0, or BASE^0 is equal to 1, for any BASE.  Why??  The short answer is, it is useful.  It works.  We will come back to the long answer.


BASE BASE NAME To exp 0 To exp 1 To exp 2

To exp 10

2 BINARY 1 2 4 1024
2.718 NATURAL 1 2.718 7,389 22,026 000
10 DECIMAL 1 10 100 10 000 000 000


A few things about this exponent shorthand.  First, there are only three bases in common use:  Base 2 (Binary) for all things computer or “IT” (Information Technology), Base 10 (Decimal) for all things everyday, and Base ε (The natural base signified by Greek letter epsilon—alt 238 on IBM—but usually changed to a lower case e for typing convenience) for all things natural and scientific.  Base e is an irrational number.  The value of e to 10 places is 2,718 281 828.  The comma is being used as a decimal point.  In use 2,718 usually suffices.  Some calculators save display space by showing something like 4,56 x 106 as 4,56E6.  You are supposed to understand and fill in the x10 part in place of the E and understand the 6 as a superscript.  It may be confusing at first, but it does save display space.  Scientific calculators usually have an EE key for Exponent Entry.  Be aware that such calculators automatically assume that the base is 10 and they are only equipped to receive integers (whole numbers, plus or minus, usually including zero).  No fractions.  No decimals.  Most of these calculators require that a negative be indicated with a special (-) key or a change-sign key, NOT with the subtract function key.  If you want to enter a non-10 base or use a fraction or decimal exponent, locate the XY key and use it.  It may appear as ^ indicating you should enter BASE^EXPONENT, for example 4^2.5= on a TI-30X IIS produces 32.  More on this below.


Hopefully, the author will always tell you what the base is.  If not, it may be clear from context.  Make your bases clear to your readers.


Adding or Subtracting with Numbers Expressed As Powers

The short answer is, you cannot.  Let us say that we are told the company annual budget will be 56,090 x 106 dollars (56 million, 90 thousand dollars).  IT informs you that it is adding an approved server purchase for $20 000.  How do you add 56 x 106 and 20 000??  You do not.  You must convert the power shorthand to a fully written number: 56 090 000 dollars.  Now you can add the 20 000 dollars.  You will get: 56 110 000 dollars. (56 million, 110 thousand dollars).  This can be written as 56,11 x 106 dollars.  An alternative is to convert the 20 000 into 0,020 x 106.  Now you can add 56,090 to 0,020 to get 56,110 x 106.  We can only add or subtract if the power suffixes are identical.  The same rule applies to metric prefixes.  If something weighs 1,23 mega gram and the packaging weighs 13 kilo gram, to get a total for shipping, we must convert both to either kilo gram or mega gram.


Multiplication in Power Format

Multiplication is a whole different story.  Say we want to double our 56,11 x 106 budget.  We just do 56,11 x 2 = 112,22 x 106 dollars, and we are done.  Now suppose we have one million of something and we want to repeat it 1000 times.  One million is 10and 1000 is 103.  Their product is 10 (6+3) = 109.  Why??  Well, we have ten multiplied 6 times and then another 3 times for a grand total of 9.  Sure enough, a million times a thousand is a billion which is 109.


Multiply by Adding—Logarithms

We have discovered a way of multiplying by adding.  In its full form it is called logarithms.  Before the creation of all these lovely pocket sized, battery operated, calculators, sales people had books of logarithms.  To multiply A x B you would find the logarithm of A, add it to the logarithms of B, and find out what number {log (A)+log(B)} represented.  That number was the product of A x B.  There are two types of logarithms: natural logs use Base e (2,718 etc.) and common logs use Base 10.  The logarithm of a number is the power you have to raise the base to in order to get that number.  So, using common (Base 10) logs, the log of 10 is 1 because 101 = 10, and the log of 100 is 2 because 102 = 100.  For commerce the Base was 10.


How about Base to the 2,5 power (Base2,5) or 1,5 power??

Reminder:  This: , is a decimal point!!

Let us start with BASE1/2, also written BASE exp ½, or BASE^1/2.  This is the square root of BASE.  If the exponent is a fraction, the numerator is a power and the denominator a root.  NOTE: FRACTION!! NOT DECIMAL!! So BASE^1/2 is the square root of BASE.   105/2 is the square root of 10 to the fifth power.  101,5 is the square root of 10 to the third power, 103/2 = (103)1/2 = 31,6 (the square root of 1000).  NOTE: THE DECIMAL WAS CONVERTED TO A FRACTION!!  To understand 10^1,5, you may well need to convert the 1,5 to 3/2.  Now you have the square root of (10 cubed), which is the square root of 1000 = 31,6.  Unless you are log scale familiar, do not try to work from the decimal.  Cherish this.  It is probably the only place in all the universe where fractions have any purpose or value.  {If you are log scale familiar 10^1.5 lies between 10 and 100 and is half a log decade up from 10.  The midpoint of a log decade is 3.1 and 10^1.5 is indeed 31.}


Your scientific calculator should understand decimal exponents such as 2,5 1,5 or whatever, perfectly well.  If not, you need a new calculator.  It is only us people who will have trouble interpreting.  (Caution: This assumes you enter numbers into the calculator using YX or ^ and not using EE or EEX.  EE and EEX and any other of their ilk automatically assume BASE = 10 and understand only integers!!!!  If you enter something like 2 EE 1.5 you will probably get something like ERR, ERROR, or SYNTAX ERROR.  These Scientifics are smart, but not that smart.)


Exponent Addition and Multiplication

We made the point earlier that to add A to B where A and B are of the form A = (C x BASE^EXPONENT), and B = (D x BASE^EXPONENT) both A and B had to have identical (BASE^EXPONENT).  The sum is then (C + D) (BASE^EXPONENT).

But now, suppose we have (BASE^EXP1) x (BASE^EXP2)  We are looking for a product, same base but different exponents. (BASE^EXP) is BASE x BASE x BASE x …EXP times.  Thus, 8 EXP 4 is 8 x 8 x 8 x 8 = 4096.  8^3 is 8 X 8 x 8 = 512.  The product of these two multiplication chains is 8 x 8 x 8 x 8 x 8 x 8 x 8 or more compactly stated, 8^7, just the sum of the exponents (4+3).  If there are coeffecients C and D before the BASES, then we get (C x D) (BASE^(EXP1+EXP2)).


For example (4,5 x 22^3) x (2,2 x 22^5) = (4,5 x 2,2) x (22^(3+5)) = 9.9(22^8) = 5,43 x 10^11, a sizeable number.


Two rules you need to remember:

When faced with nested parentheses as just above, work from the innermost outward.  Thus for the above sum EXP1 and EXP2, and then raise BASE to their sum.  If faced with a BASE raised to a BASE which itself is raised to some power, if there are parentheses follow the innermost to outer rule, if there are no parens work from the top (highest or rightmost superscript) down.  Example:  2^(2^8) = 2^256 = 1.158 x 10^77.  If you do it wrong, you get 4^8 = 65 536.  This is a gigantic difference.  Faced with 2^2^8 with no ‘parens’, following the rightmost/highest rule, we get 2^256 = 1.158 x 10^77 which is correct for no parens, so if you want some other operation order, use parens!!!


Exponents:  The full Monty—Negative Exponents

If you thought there had to be more to exponents, you are SOOO right.  So far, we have only looked at positive bases with positive exponents, both in real numbers (meaning no imaginaries).  Suppose the base is positive, but the exponent is negative.  For example, 10^-2.  This is 1/10^2 = 1/100 = 0,01.  The negative sign gives us the reciprocal of the raised base.  10^Exponent -3 = 0,001.  10^Exponent -0,5 = 0.316.  Stated another way: BASE 10 to the +2 (10^+2) = (10 x 10) = 100.  BASE 10 to the -2 (10^-2) = (1/10 x 1/10) = 0,01.  So positive exponents control the number of base multiplies and negative exponents control the number of base divides.  Suppose we have 5^3 x 5^-2.  Per the foregoing, this should be 5 x 5 x 5 ÷ 5 ÷ 5.  (The division symbol, named the obelus, ÷, alt code 0247 on windows.)  The answer is 5^1, or just 5.  If we add exponents, we get 5^(3-2) = 5^1 = 5.


So our shorthand, for all real numbers and for positive bases is correct, consistent, elegant, useful, and in short, it works.  As applied mathematicians, that is all we can ask.


Negative Bases

So what happens if the base is negative??  Here things can get very confusing.  If the exponent is a whole number, even integers (2, 4, 6, etc.) should produce a positive because our standard math is that a negative times a negative is positive.  Odd integers (1, 3, 5, etc.) should produce a negative.  But, we are at the tender mercies of the calculator.  The TI 30X IIS produces all negatives.  However, it does come up with a correct numeric, and, after the answer is delivered, the user is free to flop the sign as needed.  The TI even comes up with a correct numeric for negative base and positive non-integer exponents, such as 1.5 or 2.5 (but negative base and negative non-integer exponent produces ‘syntax error’).  Again, the sign is a task for the user.  There is also a legitimacy issue here, because interpreting  -10^1,5 as the square root of -10 cubed should produce +or- i(31,623); an imaginary number and both a + and a – root.


The Greeks were Builders

The early Greeks were builders, and those who would build must measure.  One of the first of their learnings was the theorem of Pythagoras.  This theorem applied to triangles which had one 90 degree angle.  Such an angle is called a ‘right angle’, and a triangle having one is a ‘right triangle’.  Since every triangle has to have 180 degrees total angle, a right triangle has 90 degrees combined in the two non-right angles.  Thus, once we specify an angle, all three angles are fixed.  Thus, a right triangle with a 30 degree angle has angles of 30, 60, and 90.  The shape is now totally fixed.  Specify the length of any one side and the triangle is totally defined.

(Trig may have come to the west via India and Arabia—translating from Sanskrit to Arabic to Ancient Greek, but Pythagoras is credited with C^2 = A^2 + B^2 and I find it hard to believe one could develop trig and not develop C^2 = A^2 + B^2.)


The Very Famous Pythagorean Theorem

Pythagoras learned that the sides of a right triangle a, b, and c, were related by

c-squared = a-squared plus b-squared.

c2 = a2 + b2, or in caret notation, c^2 = a^2 + b^2

So for any right triangle, if you have any two sides, you can compute the third.  c is the hypotenuse, the side opposite the 90 degree angle.


Given: a right triangle with A = 3 meters and B = 4 meters.  How large is the hypotenuse c??  a^2=9, b^2=16, a^2 + b^2 = 9 + 16 = 25 = c^2

Therefore, c = square root of 25 = 5 meters.  This can be considered the start of trigonometry.


The Triangle

Basic trigonometry deals with right triangles, just as the Pythagorean Theorem does.  Our early Greek builders realized that if you took a right triangle and specified one of the other angles, let us call it angle A, and set it, for example to 30 degrees (1/3rd of a right angle, in this case), you would have specified all three angles since they must add to 180 degrees.  So if one of them is 90 degrees, and one of them is 30 degrees, the third must be 180 -90 -30 = 60 degrees.  So the only difference between this 30-60-90 triangle and all other 30-60-90’s is size.  They are all similar but differ in size.  The angles of a triangle are usually labeled A B and C.  For a right triangle, C is used for the right angle.  A and B will add to 90 degrees.  The sides are usually labeled a b and c, each according to the angle it is opposite.  Thus the hypotenuse is opposite C, the 90 degree, and is labeled c.


Angle Measurement

There are three measurements in use for angles.  Most scientific calculators can be set for any one of them.

They are:

Degrees, Minutes, Seconds (But both my TI and HP Scientifics accept decimal degrees).  There are 360 degrees to a circle, 180 in a triangle, and 90 in a right angle.  The degree symbol ° is Alt 0176.  Each degree comprises 60 minutes.  The minute symbol is either the prime or the single quote: ‘.  Both degrees and minutes can be decimal:  30,123 degrees (30,123°) (still using the SI decimal point: ,).  For minutes, 12,34’ .  Finally each minute comprises 60 seconds:  60” (symbol, double prime or double quote.)  We owe this sexagesimal (base 60) system to the Babylonians.  Alas, they are no more, so we cannot return it.  Our time system is also Babylonian sexagesimal: hours, minutes, and seconds.

Grads, also called gradians, or gons, are each 1/400th of a circle, thus there are 100 to a right angle.  This is handy because all trig functions cycle every 90 degrees (once through a right angle).  The symbol for grad is now gon, but in the past, it has been g, gr, and grd.  The grad / gon is always decimal (no sexagesimal, you will have to get your 60’s fix from your watch).

Radians are the angle measurement units preferred by mathematicians.  There are 2 π (alt 227) radians (symbol rad) to a circle.   If the radius of a circle rotates through a 1 radian angle, its tip moves over a length R (one radius) on the circumference.  A half circle (180 degrees) is Pi (π) radians.  A right angle (90 degrees) is Pi/2 radians (π/2).   As one gets into more complex math, radians are required.


Degrees and grads (gon) present a problem.  They are very close to each other.  A wrongly set calculator will deliver up wrong answers which may appear to be correct.  This can happen with radians, but it is less likely.  Make sure your calculator is set to the angle measure you are using.  Degrees are entrenched in navigation and maps.  Radians are entrenched in math.  The grad is still around, and it is the official SI angle unit, but it is on life support.

Beginning of Trig

Image a long wood or stone beam flat on the ground.  This is the triangle b side.  At one end imagine another long beam tipping up at 30 degrees (π/6 radians) this tip up angle is the A angle, and the beam is the c side (hypotenuse).  The open side, opposite angle A is side a.  As you walk down the beams and run a plumb-bob down from c to b, thus making the plumb-bob string side a, you realize that the ratio of side a, the plumb-bob length, to side c, the tipped-up hypotenuse, is constant.  It is 0.5 (= a/c) and will be for any 30 degree angle anywhere you drop a plumb-bob.  The ratio will be different for any angle A.  We call this ratio sine (A), or for short sin (A), or on calculator buttons just sin.  It is zero for angle A = 0 degrees, (a parallel with c).  It is 1,0 for a perpendicular to c (angle A = 90 degrees, approachable but not quite allowed). Sin (45) = 0,707.  Sin (60) = 0,866.  Once you have the Pythagorean Theorem and you are building and measuring triangles, the trig relationships sort of kick you in the face.  It is hard to miss, especially with 30 degrees yielding a two-to-one between c and a.  Pythagoras dates to about 500 BC.  If trig came west fromIndiaviaArabiais about 450 AD, it took the west over 900 years to spot something poking them in the eyes.  I find this hard to believe.  I suspect independent development.


Six Named Trig Functions

There are six named trig functions, but in fact there is really only one:  sin (A) says it all.  The cosine is side b over side c (side along the angle divided by the hypotenuse).  But cos (A) = sin (90-A).  So cos is not an independent function.  Tangent is side a over side b, but this is sin (A) / cos (A);  sin (A) / cos (A) = a/c ÷ b/c = a/b = tan (A).  {{A familiar relationship is sin^2 (a) + cos^2 (a) = 1.  This comes from a^2/c^2 + b^2/c^2 = 1 which becomes a^2 + b^2 = c^2 by multiplying everything by c^2, and low and behold, the Pythagorean Theorem is with us again.}}  The remaining three functions are all reciprocals of the three we have just learned.  Cotangent (cot) is 1/tan = b/a.  Secant (sec) is 1/cos.  Cosecant (csc) is 1/sin.  My HP-49 and TI-30X do not have buttons for cot, sec, csc.  It is easy to find the reciprocal and invert it with the X-1 function, and there are better uses for buttons.


“Inverse” Functions

Pay attention here.  If you can go from angle to side a ÷ side c ratio (sine), you can take the sine and go back to the angle it came from.  Thus sin (30) is 0.5, A side a to side c ratio of 0.5 (in other words, a sine of 0.5) says we have an a angle of 30 degrees.  Scientific calculators provide sin, cos and tan, and they provide the inverse of sin, cos, and tan.  My HP-49 calls these asin, acos, and atan.  These are arcsin, arccos, and arctan, though I prefer anti-sin, anti-cos, and anti-tan.  Put a ratio in, like put 0.5 in, hit asin, and you get 30 degrees.  My TI-30, in what has to be a stupidity which makes three metric prefixes beginning with m, or medicine’s mc for micro seem almost sane, calls these inverse keys sin-1, cos-1, and tan-1.  This illogic is found on many scientific calculators.  You just have to persuade your brain that these -1 superscripts have nothing to do with exponents.  Hopefully either HP’s axxx or something like a left caret <xxx will replace these misguided notations.


There are inverse operation pairs all over math.  Subtraction is the inverse of addition.  If 3+4=7, 7-4=3.  Of course, equally addition is the inverse of subtraction.  They are a pair.  Division is the inverse of multiplication and multiplication the inverse of division.  For example, 5 x 6 = 30 and 30 ÷ 6 = 5.  Division and multiplication are a pair.  Taking a root of a number is the inverse of raising it to a power.  2,3 raised to the 3rd power is 12.167.  The third root of 12,167 is 2,3.   Another pair.  Log and antilog are a pair.


These last two pairs run into a little trouble with signs.  Raising to even powers loses the sign.  For example, both +2 and -2 yield +4 when squared.  Therefore, when we take the square root of +4, we have to state it as + or – 2, because we do not know what it once was.  This problem exists for all even powers.  There is disagreement on what the log of a negative number is and whether it even exists.  In many cases, you can just make it the same as the log of the equivalent positive number.  Thus, the log of +100 is +2 (10’s base).  The log of -100 can be set to +2.


In trig we have six more inverse pairs.  We have sine and anti sine (arcsin), cosine and anti cosine (arcos), tangent and anti tangent (arctan), cotangent and anti cotangent (arccot), secant and anti secant (arcsec), and last, cosecant and anti cosecant (arccsc).  Use arc or anti, whichever is clearer to you.  For brevity, you can even go to a simple A.  For example, asin for arcsine.  HP prefers the A which is compact and very clear.


If you need to show something like 1/sin(30), use parens: (sin(30))-1 The outer parens makes it clear that the sin function of 30 degrees is what is being inverted.


Scientific Calculators understand parens.  For example, to raise 10 to a fraction with the TI, I can enter 10^(5÷2)= and I get 316,227….  (REMINDER:  That comma is a decimal point.)  The division symbol on the TI display will be a fraction bar, not an obelus, but you get the fraction bar with the divide function symbol, which is an obelus.  Thus (4÷8)+(1÷8)= yields 0.625 (which is 5/8 in fraction form).  If you want fraction format for an answer, you need something like the HP49.









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Before modern medicine, which has given us vaccines, antibiotics, drugs such as insulin, etc., it was common for one-half of all children to die before adulthood, and for many adults to succumb to rampant disease epidemics.  A population which is highly vaccinated against a given disease is protected against epidemics of that disease. Unvaccinated individuals receive incomplete but substantial protection from that disease because of the vaccinated people all around them.  All medical procedures including vaccination, have some risk, but vaccination risk is a truly tiny thing compared to the risk of diseases like diphtheria, pertussis, tetanus, smallpox, measles, or polio. The many risk scares associated with vaccination are largely paranoid inventions. Data on vaccination is humongous because most of the population gets vaccinated.   Those who don’t get vaccinated are cheating, because they share the enormous benefits of vaccination and avoid the tiny risks. I suggest that they should be barred from public schools, libraries, and places of assembly, and cheating parents should be marked for their extreme selfishness. Adults who continue amongst us unvaccinated should also be marked for their selfish cowardice.   Homo sapiens evolved in a natural environment. We are evolved for an environment of at least some of all the elements of the periodic table. At the same time, too much of anything, including water or oxygen can make us sick or even dead. If one is worried about aluminum, one should cease using aluminum pans and cease drinking beverages from aluminum cans, rather than obsess over a handful of vaccinations spread over years. With vaccination and modern drugs, we do well against such things as smallpox, polio, flu, etc. Not so well yet against paranoia, and we are far too liberal with cheaters.

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Pat Toomey does not believe in the global warming problem.  There are three classic responses to a problem.

  1. Shoot the messenger.
  2. The Ostrich response: Put your head in the sand and say, What Problem??
  3. Meet it and defeat it.

The Republicans have tried #1.  It did not work too well.  It never does.  Pat Toomey suggests #2.  It also never works very well.  In door #3 we have Joe Sestak who will work to meet and defeat the problem.

In case you are uncertain, there really, absolutely, is a problem.  Between day and night, winter and summer, tropics and arctic it is hard to use a thermometer to tell the planet’s temperature, but nature has provided a foolproof way.  The planet averages near zero degrees Celsius.  It has lots and lots of water, and lots of ice.  When it gets colder, the ice grows.  If it gets really cold, the ice comes down the center of the USA from Canada in the form of glaciers.  If it gets warmer the ice melts.  Warmer yet and lots of ice melts, and there is a lot of ice.  So we use the Ice Thermometer.  Unfortunately, as the ice melts, the waters of Earth rise.

The real problem is melting ice, not because of the polar bears, but because we built most of the large cities on Earth right on the water.  For example, Manhattan, San Francisco, Los Angeles, Oakland, Chicago, Tokyo, Detroit, Cleveland, New Orleans, Sidney, London, and hundreds of others. This was convenient for shipping both goods and people, provided a dump for sewage, and if the water is fresh it served for drinking and irrigation. That is, Until melting ice raises the water level.  The people in New Orleans can explain this problem: ‘Drowned City Problem’.

In fact we created this melting problem.  We did it by burning one trillion barrels of oil, about twice that of coal, a bunch of natural gas (basically methane), and a few forests in about 50-100 years,  The fact that there are lots of us and we raise lots of food animals did not help.  But, if you want to believe the Sun got hotter, okay, do so.  It makes little difference.    Same ice is still melting.  Same water is still rising.  Same drowned city problem is still there.  Same solution is still needed.

The cure is not to shut down our civilization, or drastically change our life style.  First we need better efficiency and better recycling for everything.  Efficiency is its own reward, and at present use, in about 37 years we will run out of oil.  Things you do not need to use, you do not need to buy.  Less oil use is green and is economic and increases our economic and political power on the planet.  Next is a shift from oil, coal, and gas to more solar, wind, geo-thermal, water, and nuclear, but much better nuclear.  You see, first we built the bombs.  Then we has all this enriched Uranium and equipment and techniques for working it, so we said to Enrico Fermi, the physicist in charge of the first reactor (under the west stands, at Stagg Field, University of Chicago) make a reactor for commercial power generation, and he did.  No one ever studied other nuclear reactions or other designs!!  (Part of this is from personal knowledge.  I was registered at the University of Chicago, studying physics, the same time Fermi was there and I knew Dr. Fermi.)  We need improvements in safety, reduction of long life radioactives, better use of short life radiation, efficient breeding, and effective non-proliferation.  None of these objectives are scientifically impossible.

All new things need time to mature.  For example, CFL’s (Compact Florescent Lamps) began as cranky, flickery beasts, suffered early burnout, cost more.  Now, a few years downstream, I just bought a six pack of Feit 75 watt (Incandescent equivalent) daylight CFL’s for $7.65, a price of $1.28 each for a bulb that lasts 5 to 10 times longer than an incandescent, is daylight balanced unlike an incandescent, and uses only one-quarter of the electricity as a 75 watt incandescent.  What’s not to love??

Tune out the Republican nonsense here.  They are wrong on every point.  They are wrong on the tax impact, the jobs impact, the overall societal impact, etc.  On Tuesday, remember that stupidity is already vastly over-represented in congress.  Bring intelligence, integrity, military knowledge, and Sestak’s commitment-to-all-of-us, to the Senate.  Elect Joe Sestak Senator from Pennsylvania.

This was written before the Japanese Nuclear Disaster.  There were a number of things very wrong with this reactor site, and some of those may apply to USA sites.  Congress should charge a committee with investigating.  One of the Japanese problems was storing spent nuclear waste in the containment buildings. Another totally critical error was not being able to generate electricity independent of the reactors.

I thought that this problem of NO ELECTRICITY had been highlighted by the infamous USA east coast blackout, but apparently the vaccine didn’t take.  New York City found itself unable to start its generators without damaging them because their was no electricity to run the oil pump motors to lube the generator bearings.  They finally sacrificed one generator by running it without oil, thus destroying its bearings, to get electricity to start the other generators safely.  No electric generating plant should ever assume that it will always have electricity from its own generation or from outside sources.

One needs sufficient backup generation to run the control systems, to shut down all reactors, and to cool until safe from meltdown.  There should be redundant generation, redundant wiring (circle feeds), and redundant fuel storage.  There should be a helicopter pad in case additional fuel or generation is needed.  The military can be charged with maintaining fuel and  generators which they can copter to any reactor.

Reactors need to be equipped with gravity activated scram rods, and maybe with cadmium sulfate quench solution as a last ditch shutdown.

As problematic as nuclear may be, it is the only feasible near term energy solution.  We need to make it safe, but then we can say this about any of our technological systems.  In any emergency, electricity is the first thing to go.  Once electricity is gone, everything else is gone.  We need to correct this.


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Zero Sum Generates NO Wealth.
The economics of zero sum is a limited thing. Everyone knows some zero sum games, because we play them in the kitchen or the dining room: poker, gin rummy, bridge, etc. Any game where the winnings and losses are equal is a zero sum game. All the outcomes sum to zero. Even a Las Vegas game is zero sum if you add in the house take. Zero sum games neither create nor destroy wealth; they redistribute it. If a group of fixed membership, say all the wage earners in the country, plays zero sum games for ten years, at the end of the ten years, they collectively have what they started with, no more, no less. So how does an economy generate more wealth??

Benji’s in the Dark Are Illegal.
There is the Benji’s in the dark theory, explained to me by a colleague. When no one is watching, Benji’s multiply in the dark. But this is not to be trusted, because she could sight read the USA Commodities B Schedule and parse it in her head. (Hi Judy, wherever you are.) We’re talking special powers here. Also, the Secret Service frowns upon Benji’s multiplying in the dark. This could get you ten years of free room and board in a concrete facility. So let us try again.

The USA Circa 1936-to-1940.
Let me start anecdotal. I was born in 1933. I grew up in a west side Chicago neighborhood (Austin). I remember horse drawn carts selling vegetables, ice, and sharpening knives and scissors. My mother shopped at a local storefront grocery. When she wanted, say a can of peas, the proprietor reached up with a long extender grip and grabbed the can from way overhead. Well, it was way overhead for a five year old. Today OSHA probably would take one look at extender and can and close him down. No supermarkets. No frozen anything. (No freezers.) After the grocery we went to the fish market, or the meat market, and last to the bakery. If you were in school, your ride was a bicycle; probably a hand-me-down. Some folk had cars, but most made do with bus, elevated (EL or ‘L’ in Chicago speak), or streetcar. There were about 105 million of us in the USA. A TV set was a big deal. No cell phones; no mobile anything.

Function Comes from Form, or NOT??
You see something which looks different and behaves different. Example: You see a tow truck. It looks different than a normal pickup. There are two ways you can reconcile this. You can assume that the reason it can tow cars is the arm, chain, hook and winch it carries. The difference in function is due to the difference in morphology (shape). Most of us would without hesitation agree with this interpretation. You could also decide that some other hidden factor(s) made it a tow truck and these added implements were actually in the way. We would try to dissuade you of this, but now I have something sad to tell you. If you got sold this way of thinking young enough and by your parents, you are probably not going to fix. You have a form of Stockholm syndrome, and you are probably never going to fix.

Tearing the Wings Off the Bird!!
Another example, a nastier one, you observe birds fly. You love watching them. You see the wings flap all over and decide they must be in the way, so you tear them off. Instead of reading form as implementing function, you are reading all differences in form from your own preconceived image as bad. For the rest of us, the changes in form are enabling; for you they are disabling. Again, this is a head case we probably cannot fix.

Of course, you yourself don’t have this problem or you would not be reading this. But guard your head and the heads of those close to you.

Select Prime Grade Republican Geniuses

Republican Ron Johnson running for the senate as a Wisconsin republican is “glad there is global warming.” Maybe he likes swimming for his life. (Practicing the New Orleans Crawl??) He calls Social Security a giant Ponzi scheme. (What he wants to ‘Ponzi’ is probably all that Soc. Security money.) He thinks drilling in Lake Michigan is just fine. (I guess congressmen can afford bottled water.) He wants the corporations back in charge of the country. (You mean they’re NOT???) He doesn’t think we should beat up on BP. (After all, they have a smashing insanity defense.)

Sharon Angle, republican running for senate from Nevada, believes that “as your U.S. senator,” she’s “not in the business of creating jobs”. (We believe you Sharon!!) She has talked about Americans using “Second Amendment remedies” to protect themselves from this “tyrannical” government. (I didn’t realize that ‘we the people’ were tyrannical. We must mend our ways!!) She opposes abortion even in cases of rape and incest. Her advice to a 13-year-old who became pregnant by her father would be to turn a “lemon situation into lemonade” {Some lemonade!!}

Pat Toomey, republican from Pennsylvania for the senate is former president of the extremist Club for Growth. Rated by the American Conservative Union as being even more conservative than radical former Senator Rick Santorum (R-PA) He voted to give federal loans and benefits to corporations that move off shore and he supports privatizing Social Security. (Equal Aid?? Or do the ones that move offshore get a bonus??) He said that “the derivative industry has..done enormous good and has been an enormous force for positive change in our economy.” {I have never before heard anyone classify bankrupting the banks as “positive change”, but I guess we all have our private definitions.} Toomey wants to “take our country back” to the good old days when Wall Street wrote its own rules. Toomey opposes Wall Street reform, and as a trader was involved in derivatives, which many believe contributed greatly to the current financial crisis. By the way, by “good old days do you think he means the Great Depression??

Carly Fiorina is a republican running for the senate from California. As CEO, she nearly ran Hewlett-Packard into the ground, laid off 33,000 workers and was named one of the nation’s worst CEO s by Portfolio magazine. After being forced out, she collected a $42 million golden parachute. Endorsed by Sarah Palin as one of her “Mama Grizzlies”. Endorsed by Sen. Jim Inhofe of Oklahoma, who said Fiorina shares his goal of weakening the Environmental Protection Agency. Fiorina wants to “take our country back” to a time before environmental regulations. (I guess Californians have forgotten all about SMOG. What an opportunity to repeat history!!) She has pooh-poohed climate change concerns as worrying about “the weather.” (See Hot Weather Followed by a Substantial Chill.) on www.thingsfuture.com

There are lots more of these republican political geniuses.

Let us go back to economics. The economy of the United States is hands down the largest in the world. Moreover, it is the largest in the history of the planet.

Economies are the most complex things on the planet. They are effected by the weather (affecting crop production), by disease (workers get ill, farm animals die), by storms (hurricanes, tornadoes, blizzards, heavy snows), by foreign events (famine or trouble in a foreign supplier or purchaser), accidents (fires, explosions), by national mood (a saving mood / a spending mood), by international mood, by things almost without end. The economy is effected by the flow of money, both national and international. By treaties. By past shortages or overages. By future anticipations. By prohibitions (such as no more Freon 12.) By inventions, such as new cellphones. In short, everything physical dead or alive, sentient or dumb affects the economy. Economic growth results from partnership melds which deliver desired product. New product, such as iPhone, produces much growth. New product availability produces growth. For example, easier education funding results in more education being purchased, which in itself adds to the economy, and this additional education strengthens the workforce improving output.

Economists work desperately to understand all of this. Some limited progress has been made. Economists use a set of differential equations borrowed from physics. (The thermodynamic relationships.) There are economists skilled with these tools. Do not look for any Republican politicians skilled with these tools. Moreover, everything that happens has already been factored in. If the public expects the feds to change the interest rate, investors will immediately crank this in. When the change is announced, if the rate cut was less that expected (less than the anticipation), the market goes down. DOWN?? Sure. The investors had cranked a 1 point interest drop into their actions and the investors cranked this 1% into their calculation. Then the fed only went 0.5%. Its a mind game. If you can read minds, you can do very well. Expansion becomes contraction because of investor uncertainty. There is ALWAYS more money locking for a good safe return than can be placed. ALWAYS.

Uncertainty is what sinks the ship.

One of the problems with all economies is instability. The economy tends to feed on its own success or failure, cranking itself up or down. In engineer speak, there is lots of positive feedback built into the economy. Success can cause it to go red hot and inflate out of control. Failure can cause a downward spiral. Anything which builds stability in is a big help. A government program which has a flywheel effect can markedly improve stability. Social Security is such a program. A fixed amount is distributed every month, and promptly spent. Medicare also provides stability.

So now along come these Republican politicians, and they are going to pull things like wings, feathers, legs, etc. off of the bird which will make it fly better. Can anyone give me even a vague and stupid reason to believe this. This bird flies better than any other bird in the history of the planet, and these Republican pols are going to yank a few things off and improve it. They have no proof. None of them has ever actually improved a bird (improved an economy). They have written no papers. They have no computer simulations. You know, to believe them you have to be so stupid as to be certifiable. Before pulling the wings off, it would be good to know that the bird will still fly well and be stable.

All life insurance and retirement funds use early premiums to pay subsequent claims. This does not make them Ponzi schemes. The Tell of a Ponzi scheme is promising returns which can never be realized. (Like a 35% annual ROI.) Later principal is then misappropriated to pay earlier returns. The con artists say, “see, 35%”. Insurance and retirement funds are not Ponzi schemes. If they need adjustment, they can be adjusted. Most of these Republican pols wouldn’t know a Ponzi if it bit them in the ass. The rest of them want to run a Ponzi.

I would say, “exile them to Europe and let them pull the wings off some European birds, but they would probably start either a world wide depression or a world war. We could send them to Nevada and let them do nuclear processing at Yucca mountain (a favorite Sharon Angle project), but I have relatives in Nevada. I am open to suggestions provided no violence is done to the economy. Violence to these Republican pols is acceptable.

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I was enjoying my tri-daily Oreo cookies, and yes, ever since “Double Stuf” I have been a confirmed Oreo Cookie addict, when I was inspired to examine the package.  The instant that you touch it, the pliable plastic film shouts, “Do not squeeze me or you will have cookie crumbs!!”  Somehow, store employees and store customers respect this because when I open a package, almost all the fragile cookies are whole.  (If only we could do this same thing for the supermarket fruit!!)

The package opens totally without tools, no knife or scissors required, by pulling a tab on top.  Octagonal traffic-style stop signs at each end warn, “STOP—Open with pull tab on top.”  As you pull, the top flap comes up and five special plastic strands snap.  These five strands guard against tampering with the product.  If they are broken, it was already opened.  With the flap up, the cookies display before you, seeking your gaze.  There are no loose pieces of package to dispose of.  NONE!!  ZERO!!  ZIP!!  The cookies are arrayed in three long rows, cradled in a plastic tray, the second part of the package.  Cutouts in the row dividers ease removing the first cookies.  The flap reseals to protect its precious cargo.  There is no need to transfer the cookies.  The packaging is two and only two pieces, from opening to disposal, and one remains inside the other.

Red, white, and blue imagery and typography convey all the usual information and add a cheery note.  The entire package weighs about one-half ounce and holds 32 cookies weighing about 16.6 ounces, a 33-to-1 contents to packaging ratio.  When one is aching for a cookie, opening, extracting, and resealing is trivial.

Job well done Nabisco.

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