Tag Archives: mathematics

In theory, in reality

I had a dream about a year ago.  At the time, I was wholly enamored of the block-and-tackle; a system of pulleys which affords us an ease of lifting directly proportional to the amount of excess rope you are willing to pull.  In other words, it allows you to lift a 10 pound weight 1 foot by attaching a 5 pound weight at the other end which will be lowered 2 feet.  We attribute its invention to Archimedes.  I and others like to think of him as the father of engineering.

In my dream, I was pulling myself up a rock face.  My rigging, naturally, employed a block-and-tackle.  In addition, I had a spotter at the top who, on my command, would add another pulley to the system lessening my strain.  Of course, for every ounce of exertion I conserved, I had to exhaust an equally large length of rope to get me to the top.  Physics is so amusing.  Energy is always conserved.  There is no free lunch.   I don’t remember how many pulleys were involved in my ascent by the time I woke up but I know for sure I hadn’t yet reached the summit.  I had arrived however, at a conclusion that still makes me smile.

Phycisists, it seems, are fond of ignoring certain variables for the sake of exposing and isolating others.  In the case of the block-and-tackle, one would want to ignore the effects of the friction on the axle of the pulley.  In reality, it would take a little more than 5 lbs to lift the 10 lb weight because some energy would be lost to friction.  Or to put it another way, the 10 lb weight would rise a little less than 1 foot and the 5 lb weight would drop a little less than 2.

But I can still dream as the phycisist can pretend temporarily that friction doesn’t exist.  And so, upon waking, I imagined what it would mean to hoist yourself up with infinite, frictionless pulleys arranged as necessary.  Ha.  So your muscles would feel absolutely no fatigue but pulling an infinite length of rope would get you absolutely nowhere.  Slack forever.  So that’s how infinity and zero know eachother.

Now back to reality.  Time to get up and start the morning ritual.  Make some coffee before considering anything else.  Mmmmmm.  Tasty.  Now consider infinite pulleys subject to friction as per reality.  Ha.  So you could pull infinitely hard but wouldn’t be able to budge the rope a hair?  The opposite of slack.  That’s hysterical to me.

To sum up.  you cannot pull yourself up by your bootstraps.  Even with a frictionless pulley, you’re still responsible for some energy if you intend to get anywhere.

Meta Humor

Humor, in many ways, bears a strong resemblance to the first law of thermodynamics.  Namely, it can neither be created nor destroyed.  Yes, the  comedian creates his jokes but the essence of what makes them funny lies in a process; and that process is either (as chemists put it) spontaneous or it is not….it’s either funny or it’s not.  I’ve heard the phenomenon of humor analyzed in many ways but perhaps my favorite observation is regarding the pun.  Puns, one author says, cannot be invented but only discovered.  To exist they must be already embedded in the structure of our language.  Anything funny, you will find,  is only amusing because of it’s absurd, ironic or otherwise ridiculous relationship to reality.  As such, reality should be regarded the source of humor.  Truth, in fact, is stranger than fiction.

A new phenomenon in the humor market is truly splitting my sides.  To write about it will not seem funny at all but I promise you, if you catch a glimpse of it you’ll be laughing.  That is, after all, the measure is it not?

Every so often,  a phrase comes along and somewhat metaphorically takes on a well defined meaning beyond the suggestion of the actual words involved.  The cliche has become a prominent function of communication and I guarantee you’ll hear one uttered in the next day or so if not in the next hour.  What’s hysterical to me at present, is the occasion when one utters a cliche but actually means it in the literal sense.  The irony just kills me on more than one level hence the term ‘meta-humor’.

Regretfully, I can only offer one example at present  and it is quite an infantile one but I’m certain that many more exist and that they will surface if you wish to notice.  Again, to read about this is not funny but to experience it is…I think.   I was explaining something to my friends tonight and, wishing to convey his girlfriend’s approval of my opinion, this guy said ‘That’s what she said’.  Yes.  It warranted audible laughter (aka LOL).  Childish as it is, that phrase has succeeded in causing laughter on many occasions.  It speaks silently of a reference to something else and that surprising, sudden re-routing of thought makes us laugh.  That, I think is the true stuff of humor.  The irony is, that the whole thing has come full circle.  The connotation of that phrase has become so accepted (in this discrete culture of mine) that to hear those four words spoken in earnest just cracks me up.

Humor is a delightful accident is my point.  It comes about when our mind is forced to crash and laughter is it’s spontaneous result.  It is pre-existent in the languages, cultures and situations that arise and does not exist apart from them.  Today we have at our disposal a whole new encyclopedia of phrases that have taken on a life of their own.  As each is just a combination of words, they’re bound to be uttered literally at some time and, when I’m fortunate enough to witness this, I burst into laughter, uncontrollably.  Let me know if you have had this experience too.

A transcendental day


Last night I opened yet another transcendental Pandora’s box not realizing the irony of the fact that, being 2 o’clock  in the morning it was officially Pi day.   I have this rather unpractical habit you see of trying to resolve ancient mathematical paradoxes in a single evening.  It’s ambitious, while largely unproductive yet educational and entertaining all the same.

While driving home I thought it quite unsatisfactory that the year has a fractional number of days in it and so resolved to look at the numbers and see if anything could be done about dismissing leap years, normalizing the length of the months and things of this nature .  My apologies to Kepler, Galileo and the mathematical community in general for assuming this would be within my capabilities.

Half an hour after I got home I found myself entering data in the excel spreadsheet I’d created to compile all the many categories of numbers I found.  Our understanding of our position in the universe, of course, is a relative one and so even the question ‘How long is a year’ is a subjective one.  Furthermore, none of the lunar months or astronomical years I looked at were divisible by an integer number of days (or even seconds in many cases) and so I found myself once again in transcendental quicksand, with no foreseeable end to the quantity of significant digits that would suffice in pulling me out.

This afternoon I am patting myself on the head thinking ‘nice try killer’.  I will have to rank this excursion with the time I tried to calibrate integers such that Pi and Euler’s constant would be whole numbers or the time I tried to reinvent music by splitting the difference between Pythagorean tuning and Equal Temperament.  I concede for now.  1 is 1 and Pi is Pi.  Regarding musical temperament however,  I’ll get back to you.

Five fourths of Americans don’t understand fractions

Regarding my recent post, statistics on statistics, I need more votes. Granted the question is absurd, however I am planning a legitimate analysis of the data and there are, I believe, some potentially interesting conclusions to be drawn therein.  In the scientific world, statistics are regarded as mathematical facts; their purpose being the formulation and validation of assumptions that could not otherwise be ‘proven’ even by an inexhaustable amount of empirical data.  In the commercial world however, statistics play a  very different role and are interpreted with an equally distinct degree of rigor.  I don’t want to spoil the punch line but it promises to resemble something like what you see when you stand in between two mirrors.  So click on the link above and send some votes this way please.

HTML-Bridging the gap between human & machine

Amazing.  Having outgrown the customization options of the wonderful free services here at wordpress.com, I decided to venture over to their .org sister site.  Minutes later I was (virtually) knee deep in HTML tutorials and today, a mere 18 hours later I’ve written pages and pages of code defining an attractive and fully functional web-page.

I will take about 2% of the credit for this, give another 8% to the age I was brought up in for preparing me, and give the rest to the genius’ that have developed this code and the mechanisms necessary to decipher it.

I suppose I’m what ‘they’ call a newbie and I’m sure the learning curve begins to level off significantly from here on in, but that’s just the way I like it.  Entice me with instant gratification and then toss me to the wolves and see how I fare.  How could I fail though?  The language is so damn logical and, who knew what that magical menu item “page source” was for on your browser.  Learning HTML is much simpler than teaching your five year old to read is all I have to say.  Sound it out?  Sure, that works about 10% of the time.  Do you know how many different sounds the letter ‘a’ makes?

<HTML>-one tag, one meaning.</HTML>  Brilliant.  The only challenge is planning ahead and remembering to close all your “‘s and <‘s.

It is truly a credit to our great minds and not a thing to be taken for granted that we have developed a language so powerful.  The syntax is such  that a human can begin to write it with little practice and a computer can understand it provided you ‘dot your i’s and cross your t’s’ so to speak.

I don’t even have a web-host yet much less a reason to publish a site.  I’m only writing to celebrate the awakening I’ve had.  If I wanted to I could do this, or that, or this-and-that….and it would show up in your home for $6.95 a month.  Currently, I don’t have any monthly bills in the single digits and most, to tell you the truth are in the triple if not quadruple digits and so I’m enticed all over again.

All I need now is some inspiration.  Hmmmm?  What to publish and why?

Statistics on statistics

Some people say 75% of statistics are made up on the spot.  Others say it’s closer to 90%.  Please help me quantify the general consensus by voting on the converse question ‘What percentage of statistics are accurate?’  I will be publishing the results along with my analysis once I have sufficient data.  Please share with your friends.  The more data I have the merrier I will be.