A Barrier to Understanding

Most people have heard of Chuck Yeager.

This guy was the test pilot for the Bell X1-A and he was the first person to "break the sound barrier".

What that actually means is that his craft went faster than the speed of sound in air.

A lot of people who do not understand much physics ask the same question about light.

"Is there not a light barrier to break also?" they cry.

The answer is no, for the reasons specified below.

Sound travels in air, and is a vibration of air molecules.

Light travels in a vacuum.

There is no reason why an aircraft can surpass the speed of sound in air, as the effect largely is governed by the doppler effect, which is the same effect that police sirens seem to sound differently when they pass you.

But Einstein produced equations that clearly showed that anything travelling at the speed of light (except photons, which are massless) will end up with infinite mass. try pushing an infinite mass beyond the speed of light and I think it will be found that it is quite difficult.

The thing about space speed is that because mass increases the faster you go, it gets ever harder to push it. The technical way to say this is that the energy from the push goes to increase the mass, not the speed.

The more you push, the more of your push goes into the mass increase.

Oh, and another thing, if your craft gets very near the speed of light, time stops for it.

Alexander the Great did not Exist AND he had an Infinite Number of Limbs.

NOTE TO READERS - I bet 0.5 KRW that this gets at least one serious comment.

NOTE TO THE INSANE - this article was actually published in a book.

NOTE TO THE INTERESTED - this is what we get up to when the beer runs out.


I Quote:

"Bertrand Russell has defined mathematics as the science in which we never know what we are talking about or whether what we are saying is true. Mathematics has been shown to apply widely in many other scientific fields. Hence, most other scientists do not know what they are talking about or whether what they are saying is true. Thus, providing a rigorous basis for philosophical insights is one of the main functions of mathematical proofs.

To illustrate the various methods of proof we give an example of a logical system.

The perjorative calculus

Lemma 1: All horses are the same colour.

Proof by induction:

It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour. Q.E.D.

Theorem 1: Every horse has an infinite number of legs.

Proof by intimidation:

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 colour, and by the lemma that does not exist. Q.E.D.

Corollary 1: Everything is the same colour.

Proof:

The proof of Lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional "For all x, if x is a horse, then x is the same colour," namely "is a horse" may be generalized to "is anything" without affecting the validity of the proof; hence, "for all x, if x is anything, x is the same colour." Q.E.D.

Corollary 2: Everything is white.

Proof:

If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular then: "for all x, if x is an elephant, then x is the same colour" is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain's The Stolen White Elephant). Therefore all elephants are white. By corollary 1 everything is white. Q.E.D.

Theorem 2: Alexander the Great did not exist and he had an infinite number of limbs.

Proof:

We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, "If Alexander the Great existed, then he rode a black horse Bucephalus." But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist.

We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and "forewarned is four-armed." This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs. Q.E.D.

It is not to be thought that there are not other types of proofs, which in print shops are recorded on the proof sheets. There is the bullet proof and the proof of the pudding. Finally, there is 200 proof, a most potent spirit among mathematicians and people alike."

Unquote.


Aki's Choralarry:

"All infinitely white horses of the same color belong to either an indefinite number of horses' legs or Alexander the Great."

Spank Me

Here is a true story. Way back in the 60's, when atom smashing was just starting, it was thought that the basic building blocks of matter were not really that basic after all.

Protons and neutrons were bashed together so violently that they acted like they were made of smaller bits.

These bits were named "quarks", after the word from the book Finnegan's Wake. At first, two were enough to explain all of normal matter, and we called the "up" and "down" quarks. However, strange things started to happen soon after.

Literally.

Particles flew out which did not behave as they should have. Then to add insult to injury, us scientists added to the "up" ans "down" quarks another "flavor" of quark.

We called these strange particles "strange" particles.

This one was much heavier than the previous two, so it took much more energy to produce it.

The prediction was then made of a further "flavor" of quark, available at still higher energies.

Once again, our verbosity got the better of us and we named it "charm".

This quark first appeared in what we lovingly called a "charmonium" - a particle made up of one charm and it's antiparticle.

To scientists, this was not good enough - we wanted pure charm, ie charm on it's own. So the search for "bare charm" was begun.

As the energy of the accelerators increased, sure enough, bare charm was found.

That brought the quarks to four (up, down, strange, charmed).

It gets even funnier. The theorists told us that the had figured out that there were no more than a total of six.

So we got our thinking caps on again and came up with two more wonderful names - "bottom", and "top" , each one still heavier than the last. At first, we found the "bottom" quark, then eventually, the "top"

Imagine the remarks that were made when we tried searching for "bare bottom".

That just about sums it up really

Communications Breakdown

This is the basis of global communications in the present day.

In simple terms, it is an object in orbit. Search on "explanation of orbit" in this blog to find out what "orbit" actually is.

Communications Satellites have special orbits. It all happens because someone realised that if the object is high enough, it can circle the earth at the same speed that the earth itself rotates. Sadly, it was never patented.

The practical upshot of which is that when viewed from the ground, the object will be above the same spot at all times.

For this reason, the are called "stationary orbits". and are now the basis for communication, TV and SatNav.

All because we know exactly where these things are all the time.

And was it who had this idea?

None other than 2001 author, Arthur C.Clarke.

(100 bonus points for each of the three meanings to the title of this post)

I am still Partial to a bit of Calculus

One of the most pervading formulas in all Physics. This is the wave equation.

It is a partial differential equation of the second order.

There are four things that wiggle.

Time, t, and the three spatial coordinates x, y, and z.

So where are they? The formula is in shorthand because it is used so often.

"c" is the speed of the wave.

"u" is the part (made up of "t"'s) that tells us how the wave changes over time. The double dots reminds us that is a second order differential.

Now comes the interesting bit.

The triangle is a capital Greek letter call "nabla".

It is shorthand for the way the wave moves through space. we call it the "del operator" and gives the instructions about how the "u" changes in space.

It is short for





The squiggly "d"'s are there to remind us that this is a partial differential, and the x, y, and z with hats on are telling us which way to point the value of the stuff after them.

This equation is quite general, but has applications wherever waves of any kind are to be found.

The quantum mechanical pearl that is the Shrodinger Equation is just one application.

".....Nor any Drop to Drink"

It is fairly safe to say that everyone has at least heard of radioactivity.

But what exactly IS it?

Well, it is a bit like the commercial for Red Rock Strong Lager - "It is not red, and there are no rocks in it"

"radioactivity" is similar - "It has nothing to do with radios, and it is not about activity, but the lack of it"

Scientists discovered it because it kept making them very ill.

When we studied it, we found there were three basic types. We called them after the first three letters of the Greek alphabet, Alpha, Beta and Gamma (our word "alphabet" came from the joining of the first two)

They were classed according to how dangerous they were.

Alpha - stopped by paper
.
Beta - stopped not by paper but tin foil.

Gamma - stopped only by several centimeters of lead (about 10)

But what were they?

By doing various esoteric experiments it turned out they were:

Alpha - Helium nuclei (to protons, two neutrons)

Beta - electrons (or their antiparticles, positrons)

Gamma - very high energy light rays (electromagnetic radiation)

The danger?

Alpha - forget it

Beta - Don't go swimming in a pool that glows blue (yes, GLOWS) If you do, it will be an atomic reactor and the glow is because the electrons are traveling faster than the speed of light in water.

Gamma - Be at least 12 miles from an atomic bomb

The danger is the damage gamma rays do. It is at the cellular level, which means that gamma rays are so powerful they pass right through you, except if they hit the nucleus of a cell (nothing to do with an atomic nucleus).

The danger of that is that if a cell is damaged, there is a very high probability of contracting cancer.

The fact that many people do not realise is that the effects of radiation poisoning are cumulative, rather like the way an hourglass works. Over time, the sand builds up in the bottom half.

Radiation is the same. There will come a point when the poisoning has "built up" so much that exposure to more will be really dangerous.

We wear badges that tell us how much "sand" has passed though us. In that sense, our work is very dangerous.

In the opposite sense, our work is very safe, simply because it is controlled.

Having said that, the door to the experimental area is a 2-meter by 1-meter by 1-meter tank of water.

English Marauder

This is a reflection on the day this blog started.

"Irish Invader" is my choice this time. £10 to win or £2 each way.

Either will win my bet.

"Popes, Camillas and Horses - but not necessarily in that order" was just about four years ago.

Tonight I will watch it from a hotel in Korea.

Last time I watched, there was no Ben.

However, I picked a winner, and I am not talking about the National.