Category Archives: Uncategorized

Punctuation puzzles

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A relatively obscure puzzle category is that of punctuation puzzles. An example is to add capitalization and punctuation to the following list of words to make them grammatically correct – and explain what the result means.

time flies you can’t they move to fast.

The answer is:

“Time flies!”

“You can’t. They move too fast.”

Someone asked a friend to time how fast houseflies move. The friend replied that they darted about too quickly for him to do so.

Corny? Sure. But here’s one that is a little more challenging.

becky while tom had had had had had had had had had had had the teachers approval

I will share the solution in my next post.

© 2016 Lyndon Hardy

An untold tale about Richard Feynman

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When I was at Caltech, Richard Feynman, the renowned physicist, gave a one-hour seminar each week entitled Physics X. It was not in the catalogue. There was no college credit. You just showed up in the lecture hall and Feynman would ask, “OK, what shall we discuss today?”

He was a great lecturer. With no preparation ahead of time, he would explain some hard to understand aspect of physics that was wonderfully clear. You took notes furiously, because a half-hour or so after leaving the hall, the brilliant insight that you thought you now grasped would begin to fade.

I remember to this day that one time on of us sitting in the audience said something like the following:

“Professor Feynman, suppose you are in a spaceship going very nearly the speed of light. You are flying parallel to a long mirror extending far into space alongside you. You look out and see your reflection in the mirror.

“Now it take some time, not much, but some time for the light from your spaceship to travel to the mirror and then bounce back to you. This means that the reflection will not be exactly aligned but lag behind slightly. Since you, yourself, are going so swiftly, the angle would be noticable. You would have to crane your neck to see your reflection.

“So by measuring the angle of the lag, you could then figure out how fast you are going, and that would violate Special Relativity.”

“An interesting problem,” Feynman said and retreated to the long blackboard behind him. He drew a chalk line from left to right and turned to smile at us, “That is the mirror,” he said. Then somewhere in the middle of the board, he drew a little crude spaceship, a beam of light exiting from it and the reflection coming back.

Then he calculated for a few minutes and presented the results of his calculation, an equation for what the angle would be as a function of how fast the spaceship was moving.

“Very good, young man, you are right. You can tell how fast you are going. Special Relativity is wrong.”

There was a stunned silence. How could this possibly be? Special Relativity was a fundamental cornerstone of physics. It had been around for almost sixty years. Validated by scores if not hundreds of independent experiments by the greatest minds in the world. How could an undergrad, a freshman no less, come up with a thought experiment that crashed everything down?

For a few moments, no one dared speak. Then Feynman cocked his head to the side and returned to the board. He corrected one of his intermediate equations, fixed up the results and turned back to address us. I made a simple error. The angle is independent of the spacecraft’s speed. Special Relativity is saved.”

Everyone laughed at what had just transpired. Of course, no freshman was going to bring all of physics crashing down. If I or anyone else in the room had come up with the formula for what the lag angle would be, we would have checked our work probably a dozen times before making any pronouncements to a room filled with other (aspiring) physicists.

On further thought, what had happened was pure Richard Feynman. The utter unlikelihood of a freshman coming up with something that would completely upset all of physics must have never entered his mind. Instinctively, he just followed where the equations were leading him. And to me, that was an example of what it took to make true breakthroughs, to be a Nobel Prize winner – ignore the shackles that constrain our thinking onto paths that have been traveled many times before. Who knows what wondrous thoughts might then result.

© 2016 Lyndon M. Hardy

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Time Travel and Eclipses

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Caution! Before reading further, please review the definition of ‘tongue in cheek’.

Time travel is a staple of science fiction, and with good reason. The paradoxes are delicious to contemplate.

And somewhat related, already there is quite a lot of interest building about the total eclipse of the sun that is due to be visible over a wide swath of the United States on August 21, 2017. I will be in Oregon and already have my fingers crossed that there will be no clouds.

Time Travel

Is such a thing possible? The answer depends on which way you are going—forward or back.

If you go forward, yes, time travel is possible. According to special relativity, we observe the clocks of someone moving relative to us as running more slowly. This fact leads to what is called the twin paradox. One brother blasts off into space while the other remains behind. Each sees the clock of the other running slower. After, say, may years, the spacefarer returns to visit his earth-borne sibling. So, which is now the younger?

It is the traveler who is younger. Among other places, the reason is explained here. In the reference, the stay-at-home twin ages twenty years while the traveler ages sixteen. Effectively the traveler has traveled four years into the future.

Going backwards presents paradoxes too. The classic is to figure out what happens when someone goes back in time and kills his own father before he is born. Physicists say that backwards time travel clearly is impossible. It allows things like the death of a father to happen before they can be caused—by among other things the birth of the murderer. A more folksy argument is ‘If backward time travel is possible, then how come we don’t meet any of the travelers?’

Well, think about it for a moment. Maybe, just maybe, an effect does not always have a cause occurring first and we just have not figured this out yet. And backwards time travelers certainly would be briefed not to do anything stupid. If they were really careful, everything would be OK.

But being careful can be a hard thing to do. Consider fashion, for example. It is changing all the time. Even with the internet, keeping track of the coming and going of fads is not easy. And maybe the time travel machines are not very precise. One might want to visit the sixties but arrive in the twenties instead. As soon as the traveler stepped outside of his machine, he would be immediately spotted as being very much out of place.

For women time travels this is indeed a problem, but for men there is a work around—tuxedos. Yes, men’s fashion does change too, but much more slowly than it does for women. A tux from the twenties might well pass in the sixties with little or no comment.

This means that if you indeed are looking for evidence of time travelers, going to the opera or Nobel Prize ceremonies would be a good thing to do.

Eclipses

There can be other visitors among us as well. Consider the phenomenon of a solar eclipse.

First of all, for such a tiny planet as our Earth, our moon is relatively enormous. From anywhere on the surface, it is one of the two biggest sights in the solar system. That alone is worth the visit of alien tourists.

But the fanstasic thing is that, in addition, the moon is precisely the right distance away from the sun so that a total eclipse can occur. No mere transit across the blazing solar disk, no overlap that is wasted. The moon is blocks out all of the sunlight except for a tiny ring around the edge.

This has got to be an astronomical rarity. What are the odds of such a thing happening? There very well may be no other instance in our entire galaxy. Visiting the Earth during a solar eclipse has got to be on the alien top ten list of things to do.

So, If you have a change to be in the path of totally, please follow up on it. You might see the best of all. There right before your eyes, dressed in a tuxedo, a time traveling alien.

PS

Time travel and eclipses (well, occultations) are an element of Magic Times Three

© 2019 Lyndon M. Hardy