Math Rocks!! (and physics)

(Actually, for those of you who will research this and complain to me that it's not true, hold your horses. The only thing I've really proved is that the product of the slopes of perpendicular lines does not always equal -1.)

Q. What did the circle say to the tangent line?
A. Stop touching me.

There are 3 kinds of people:

1. Those who can count.
2. Those who can't count...

There are 10 kinds of people:

• 1 - Those who know binary.
• 10 - Those who don't know binary...

Interesting proofs:

1. Theorem 1: The less you know, the more you make.
   Proof:
   • Postulate 1: Knowledge is Power.
   • Postulate 2: Time is Money.
   • As every engineer knows: "Power = Work / Time"
   • Because "Knowledge = Power" and "Time = Money", it is therefore true that Knowledge = Work / Money
   • Solving for "Money", we get: "Money = Work / Knowledge"
   • Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.

2. Theorem 2. Every horse has an infinite number of legs. (Proof by intimidation.)
   Proof:
   • Horses have an even number of legs.
   • Behind they have two legs and in front they have fore legs.
   • This makes six legs, which is certainly an odd number of legs for a horse.
   • But the only number that is both odd and even is infinity.
   • Therefore horses have an infinite number of legs.

   Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another color, and by this lemma that does not exist.

3. Theorem 3: All girls are evil.
   Proof:
   • Postulate 1: Girls require time and money.
   • Postulate 2: Time is Money.
   • Postulate 3: Money is the root of all evil.
   • "Girls = Time * Money"
   • By Postulate 2, "Time = Money", so "Girls = Money^2"
   • Since "Money = Evil^.5", "Girls = Evil"

.....6666666666666739 x 3 = 217?? (first number has 6's going on to infinity towards the left)

Several scientists were asked to prove that all odd integers higher than 2 are prime:

• Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.
• Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime. Just to be sure, try several randomly chosen numbers: 17 is a prime, 23 is a prime...
• Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an approximation to a prime, 11 is a prime...
• Programmer (reading the output on the screen): 3 is a prime, 3 is a prime, 3 a is prime, 3 is a prime...
• Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet...
• Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it...
• Chemist: What's a prime?
• Politician: "Some numbers are prime.. but the goal is to create a kinder, gentler society where all numbers are prime..."
• Programmer: "Wait a minute, I think I have an algorithm from Knuth on finding prime numbers... just a little bit longer, I've found the last bug... no, that's not it... ya know, I think there may be a compiler bug here - oh, did you want IEEE-998.0334 rounding or not? - was that in the spec? - hold on, I've almost got it - I was up all night working on this program, ya know... now if management would just get me that new workstation that just came out, I'd be done by now... etc., etc..."

You enter the laboratory and see an experiment. How will you know which class is it?

• If it's green and wiggles, it's biology.
• If it stinks, it's chemistry.
• If it doesn't work, it's physics.

Seen on the door to a light-wave lab:
"CAUTION! Do not look into laser with remaining good eye."

Absolute zero is cool.

Gravitation can not be held resposible for people falling in love.

Teachers' remarks that changed the history of physics:

• Copernicus, when will you understand that you are not the center of the world??
• Galileo, if you continue to drop stones from the top of the tower one more time, you will be dismissed forever.
• Kepler, till when will you stare at the sky??
• Newton, will you please stop idling away under the apple tree??
• Ohm, must you resist Ampere's opinions on current events??
• Nikola Tesla, I see that everyone is attracted to your magnetic personality.
• Schr�dinger, stop abusing cats!!
• Heisenberg, when will you be sure of yourself??

The difference between an introvert and extrovert mathematicians is:

• An introvert mathematician looks at his shoes while talking to you.
• An extrovert mathematician looks at your shoes.

Philosophy is a game with objectives and no rules.
Mathematics is a game with rules and no objectives.

Chemistry is physics without thought.
Mathematics is physics without purpose.

• Biologists think they are biochemists,
• Biochemists think they are Physical Chemists,
• Physical Chemists think they are Physicists,
• Physicists think they are Gods,
• And God thinks he is a Mathematician.

To the optimist, the glass is half full.
To the pessimist, the glass is half empty.
To the engineer, the glass is twice as big as it needs to be.

Q: Why did the chicken cross the Moebius strip?
A: To get to the other ... er, um ...

Why did the chicken cross the road?

• Aristotle: It is the nature of chickens to cross roads.
• Issac Newton: Chickens at rest tend to stay at rest; chickens in motion tend to cross roads.
• Albert Einstein: Whether the chicken crossed the road or the road moved beneath the chicken depends on your frame of reference.
• Werner Heisenberg: We are not sure which side of the road the chicken was on, but it was moving very fast.
• Wolfgang Pauli: There already was a chicken on this side of the road.

How many mathematicians does it take to change a light bulb?

• None. It's left to the reader as an exercise.
• None. The answer is intuitively obvious.
• One. He gives it to four programmers, thereby simplifying the problem to a previous question.

• None. They can't do it, but they can easily prove that it can be done.

• I don't know the exact number, but I am sure it must be some rather elegant prime.

• Eleven. One to do it and ten to co-author the paper.

How many astronomers does it take to change a light bulb?

• None, astronomers prefer the dark.

How many radio astronomers does it take to change a light bulb?

• None. They are not interested in that short wave stuff.

How many general relativists does it take to change a light bulb?

• Two. One holds the bulb, while the other rotates the universe.

A mathematician, a biologist and a physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street.
First they see two people going into the house. Time passes. After a while they notice three persons coming out of the house.
The physicist: "The measurement wasn't accurate."
The biologists: "They have reproduced".
The mathematician: "If now exactly one person enters the house then it will be empty again."

A mathematician went insane and believed that he was the differentiation operator. His friends had him placed in a mental hospital until he got better. All day he would go around frightening the other patients by staring at them and saying, "I differentiate you!"
One day he met a new patient, and true to form he stared at him and said, "I differentiate you!", but for once, his victim's expression didn't change. Surprised, the mathematician marshalled his energies, stared fiercely at the new patient and said loudly, "I differentiate you!", but still the other man had no reaction. Finally, in frustration, the mathematician screamed out, "I DIFFERENTIATE YOU!" The new patient calmly looked up and said, "You can differentiate me all you like: I'm e to the x."

An engineer dies and reports to the pearly gates. St. Peter checks his dossier and says, "Ah, you're an engineer -- you're in the wrong place."
So the engineer reports to the gates of hell and is let in. Pretty soon, the engineer gets dissatisfied with the level of comfort in hell, and starts designing and building improvements. After a while, they've got air conditioning and flush toilets and escalators, and the engineer is a pretty popular guy.
One day God calls Satan up on the telephone and says with a sneer, "So, how's it going down there in hell?"
Satan replies, "Hey, things are going great. We've got air conditioning and flush toilets and escalators, and there's no telling what this engineer is going to come up with next."
God replies, "What??? You've got an engineer? That's a mistake -- he should never have gotten down there send him up here."
Satan says, "No way. I like having an engineer on the staff, and I'm keeping him."
God says, "Send him back up here or I'll sue."
Satan laughs uproariously and answers, "Yeah, right. And just where are YOU going to get a lawyer?"

You Might Be a Mathematician if...

• you are fascinated by the equation e^(i*pi)+1=0.
• you know by heart the first fifty digits of pi.
• the word "polar" triggers the thought "angle" rather than "cold".
• you have tried to prove Fermat's Last Theorem.
• you know ten ways to prove Pythagoras' Theorem.
• your telephone number is the sum of two prime numbers.
• you have calculated that the World Series actually diverges.
• you are sure that differential equations are a very useful tool.
• you comment to your wife that her straight hair is nice and parallel.
• you tear out the answers in the back of the book
• before finding the answer, you first wonder whether the problem HAS a solution
• you pay those bills with prime dates first

You Might Be a Physicist if...

• the water in your kettle is boiling at 373 Kelvin.
• you know that the speed of light is 2.99792458 * 10^8 m/s.
• you know the direction the water swirls when you flush. (counterclockwise in the northern hemisphere)
• you've already calculated how much you earn per second.
• you are sure that differential equations are a very useful tool.
• you are at an air show and know how fast the skydivers are falling.
• you know the second law of thermodynamics, but not your own shirt size.
• you avoid stirring your coffee because you don't want to increase the entropy of the universe.
• you try to explain entropy to strangers at your table during casual dinner conversation.
• your three year old son asks why the sky is blue and you try to explain atmospheric absorption theory.
• you carry on a one-hour debate over the expected results of an experiment that actually takes five minutes to run.

Mathematics Revisited

• Life is complex. It has real and imaginary components.
• What keeps a square from moving? Square roots, of course.
• It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest.
• I heard that parallel lines actually do meet, but they are very discrete.
• In modern mathematics, algebra has become so important that numbers will soon only have symbolic meaning.
• Isn't it meaningless to speak of a 45 degrees angle unless you specify Fahrenheit or Celcius?

Physics Revisited

• It would be a poor thing to be an atom in a universe without physicists, and physicists are made of atoms. A physicist is an atom's way of knowing about atoms.
• When people run around and around in circles, we say they are crazy. When planets do it, we say they are orbitting.
• The moon is more useful than the sun, because the moon shines at night when you want the light, whereas the sun shines during the day when you don't need it.

27 ways to use a barometer to find the height of a building

1. Tie a long piece of string to the barometer. Hold one end of the string from the top of the building, so that the end of the barometer barely clears the ground. Give the barometer a small displacement and time its period as a compound pendulum.

2. Smash the barometer on the roof of the building and time how long it takes for the mercury to drip down the wall of the building to the ground. Use the known viscosity of mercury to find the velocity.

3. Throw the barometer horizontally off the building with a known velocity (calibrate your throwing ability by timing and measuring barometer throws on the ground). Use projectile motion to find the height of the building once the distance the barometer lands from the building is found.

4. Find a small, very efficient, very light electric motor. Weigh the barometer. Use the motor to carry the barometer up the building. Using a voltmeter and ammeter, calculate the work done by the motor, and thus the gravitational potential difference between the top and bottom of the building. Knowing g, find the height.

5. Go to the basement. Find a part of the basement such that directly above you is solid brick until you reach the roof. Throw the barometer at the ceiling of the basement, which is the floor of the building. The barometer will most likely bounce off the floor. Repeat n times, where n is a very large number. In a few trials, the barometer will tunnel through the potential field of the bricks, and appear on the top of the building. Calculate the percentage of trials for which the barometer tunnels. Use the quantum tunneling equation to calculate the length of the barrier, and thus the height of the building. Note: this effect can be calibrated properly by finding the likelihood of the barometer tunneling through one brick.

6. Attach a copper wire to the top of the building, and attach the other end to the ground. Smash the barometer and use one of the shards of glass to cut the wire halfway up the building and place an ammeter in series with the wire. Knowing the current through the wire and the resistivity of copper, the potential difference between the top of the building and the bottom of the building can be found. This will be a gravitational potential difference, not an electrical one, but the electrons don't know that. Thus, since g is known, the height of the building can be found.

7. Find a large wooden rod a bit longer than the building is high. Wrap an insulated copper wire around this rod at a uniform turn density. Make the coil stop at the top and bottom of the building. Run alternating current through the coil, measure current and voltage, and determine the inductance of the coil. Place the barometer in series with the coil so the resistance of the circuit is enough to stop the wires from melting. With the inductance of the coil and its turns per unit length and radius, the length of the coil, and thus the height of the building, can be found.

8. Drop the barometer off the top of the building and measure the radius of the resulting puddle of mercury.

9. Using a device that can propel an object at a known velocity (such as a baseball pitching machine or a rail gun), find the escape velocity of the barometer from the ground, after first having tied a string to the barometer so it can be retrieved from deep space. Repeat on the top of the building. The difference in escape velocity energies gives the gravitational potential difference between the ground and the roof, thus yielding the height.

10. Using the aforementioned pitching machine or rail gun, find the velocity at which the barometer needs to be projected to reach the roof from the ground.

11. Make a small hole in the barometer through which mercury drips at a constant rate. Time this rate at the ground. Place the barometer on the roof and observe the drip rate from the ground with binoculars. The drip rate will be dilated, by general relativity, by a factor which will give the difference in the curvature of space at the bottom and top of the building. Knowing the mass and radius of the earth and so on, the height of the building can be found.

12. THIS METHOD USES MORE THAN ONE BAROMETER: Pack as many barometers as possible into the building until it undergoes gravitational collapse and becomes a black hole. Knowing the number of barometers used, the mass of this hole can be calculated, and the Schwarzchild radius of the hole is thus half the height of the building.

13. Find a barometer that uses a liquid with no surface tension whatsoever (superfluid helium?). Break the barometer and spread the liquid evenly over the surface of the building. Measure the depth of the resulting liquid film. Knowing the volume of the barometer, this gives the surface area of the building, which will give its height, if its width and depth are known.

14. Stand on the roof of the building. Throw the barometer to a point exactly on the horizon. Measure the distance from the bottom of the building to the barometer. This gives the horizon distance at the top of the building, thus giving its height above the ground.

15. Make a small hole in the barometer so mercury drips out at a constant rate. Place the barometer so that it is dripping off the roof onto the ground. Measure the time between a drop being released from the barometer and the drop hitting the ground. Repeat the measurement when moving towards the ground at a known velocity. The time between a drop being released and a drop hitting the ground will change. Using the Lorentz transformation equations and taking the top of the tower as x = 0, the position of the ground can be found. This will yield the height of the tower.

16. Find a steel cable. Attach it to the barometer and use the barometer as a physical pendulum to measure g. Then attach the building to the cable (after having remove it from its foundations and attaching the cable to a crane of some sort), and using the building as a physical pendulum, and knowing g, measure its moment of inertia. This will give the dimensions of the building and so on.

17. Use a barometer containing sulfuric acid. Break the barometer on the roof of the building and time how long it takes the acid to eat its way down to the ground.

18. Measure the volume of the barometer at the bottom and top of the building. By knowing the coefficient of thermal expansion of glass, the temperature difference between the top and bottom can be calculated. Refer this to known data of atmospheric temperature as a function of height.

19. Every time somebody walks into or out of the building, stab them with the sharpened end of the barometer (after having sharpened it, of course). Word of the 'Barometer Murderer' will eventually reach the building's owner, who will of course be forced to sell the building. The real estate advertisement should give the height of the building.

20. Knowing the density, width and length of the building, rip the building from its foundations and place it on top of the barometer, giving it a pressure equal to the building's weight divided by the measurement area of the barometer. Thus the weight, and so the height, of the building can be found.

21. Find the architect who designed the building, crack the (mercury) barometer over his coffee, watch him die when he drinks it, then steal the building's specifications, including height.

22. THIS ALSO REQUIRES MORE THAN ONE BAROMETER: knowing Young's Modulus for brick, place barometers on the roof until the roof is lowered by one barometer length. This change in the height of the building under a known stress and Young's Modulus will give the height of the building.

23. Place a cat on top of the building. Prod it with the barometer so that it falls off the roof. See whether the cat dies when it hits the ground. Repeat n times, where n>>{a large number}. Refer to Dr Karl Kruszelnicki's paper on the probability of a cat dying when falling from a certain height.

24. AGAIN, MORE THAN ONE BAROMETER: place as many barometers in the building as will fit. This gives the volume, thus the height, if other dimensions are known.

25. Use a machine (such as the aforementioned baseball pitching machine or rail gun) that can hurl the barometer down from the ground into a hole in the ground at a velocity that is only known to within a certain tolerance. Find the smallest uncertainty in velocity, and thus momentum, such that the barometer appears on top of the building. Use Heisenburg's position-momentum uncertainty relationship to find the height of the building.

26. Tie a string to the barometer and hang it as a plumb bob. The string will be slightly deflected from the vertical by the gravitational effect of the building. This gives the mass of the building, etc.

27. Find at what velocity you must move upwards or downwards past the building such that the building is contracted to the same length as the barometer. Find gamma for this velocity, multiply by the length of the barometer.

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