My Antibirthday Occurs at Midnight Tonight


Clearly, this requires some explanation.

January 12 is my birthday, and today is July 13, 2015.

  • Remaining days in January, after today: 19
  • Days in February through June, this year, which isn’t a leap year: 28 + 31 + 30 + 31 + 30 = 150
  • Days in July up to, and including, today: 13
  • Total days after my last birthday, up to and including today: 19 + 150 + 13 = 182

How long until my next birthday, starting at midnight, tonight?

  • The rest of July: 18 days
  • August through December: 31 + 30 + 31 + 30 + 31 = 153
  • Pre-birthday January days: 11
  • Total days between today and my next birthday: 18 + 153 + 11 = 182, also.

Since the number of days between the end of my last birthday, and midnight tonight, is exactly the same as my number of pre-birthday days which follow midnight, it follows that midnight tonight is the one point in time, this year, which is as far away from my birthday as one can get, on the calendar. The fact that antibirthdays are usually points in time, rather than full days, is a consequence of the fact that most years have an odd number of days. Subtract one for my birthday (or anyone’s, except for those rare people born on February 29 — we’ll get to them later), and 364 days remain in most years. Divide this by two, and there are 182 days to fall on either side of an antibirthday midnight, for most people, during most years.

Next year, 2016, is a leap year. What will happen to my antibirthday next year, then, with its 366 days? As it turns out, next year’s antibirthday, for me, will be a full day. Why? Adding “leap day” makes it necessary to subtract two days, rather than just one, to get 364. (An even number of post-subtraction days is needed for divisibility, by two, with no remainder.) My antibirthday in 2016 will be on July 13, all day long, because there are 182 days between that day and both of my nearest birthdays — one in that antibirthday’s near past, and one in its near future.

If we don’t have the same birthday, and you want to figure out when your own antibirthday is, you can follow the pattern above, with only minor adjustments, if your birthday, like mine, falls on or before February 28. Some additional adjustments will be needed for those with birthdays in March through December, though. Why it that? Simple: my birthday occurs before February, and this isn’t true for most people. My full-day antibirthdays occur during leap years only because of this fact. If your birthday occurs after February is over, you’ll still get full-day antibirthdays every four years, but those years won’t be leap years — they’ll be one year removed from leap years, instead. Whether this means such years will immediately precede, or follow, leap years is left as an exercise for the reader.

There’s a small group of people for whom this gets even more complicated: those whose birthdays only happen every four years, on “leap day,” February 29th. Of the people I know well, only one of them, my friend Todd, was born on a leap day, and, just to be a pest, I’m going to assign him the problem of figuring out his own antibirthdays. After all, he has plenty of time for this, since the fact that he only has a birthday every four years causes him to age at 25% of the normal rate. He looks only a bit older than me, having had only a few more birthdays that I’ve had, even though he was born in 1812, and can remember the American Civil War clearly. Fortunately for him, he was still a child in the 1860s, and this saved him from actually having to fight in that war, or any other. It must be nice to have a 280-year life expectancy, Todd!

[Image credit: before turning the birthday-cake picture above upside-down, I downloaded it from this website.]

Does Everything Move at the Speed of Light?

everything moves at c

I have a friend who once explained to me his way of understanding spacetime, and what Einstein discovered about it, which was to start with the idea that, as he put it, “everything is traveling at c,” and proceed from there. Light travels at c, of course, but time does not pass for light, forming vector AG, shown in purple. A spatially-stationary rock is still traveling — temporally, into the future, at a rate of sixty seconds per minute, as represented by dark green vector AN. My friend’s idea was to interpret this rate of time-passage — the normal time passage-rate we generally experience — as another form of c. Sublight moving objects are moving at c, according to this idea, as a vector sum of temporal and spatial velocities. In this diagram, all spatial dimensions are collapsed into one direction (parallel to the x-axis), while time runs up (never down) the y-axis, into the future (never the past).

I don’t know why it took me perhaps a decade to see that my friend’s idea is testable. Better than that, the data needed to test it already exist! All I need to do is cross-check the predictions of my friend’s idea against a thoroughly-tested formula regarding relativistic time dilation. The relevant equation for time dilation is this one, which you can find in any decent Physics textbook:

equation for time dilation

In the diagram at the top of this post, the blue horizontal component-vector NM represents a spatial velocity of (c)sin(10º) = 0.173648c. It is a component of the total velocity of the object represented by blue vector AM, which is, if my friend is correct, is c, as a vector-sum total velocity — the sum, that is, of temporal and spatial velocities. By the equation shown above, then, the measured elapsed time for an event — say, the “minute,” in “seconds per minute” — to take place, at an object with that speed, as measured by a stationary observer, should be 1/sqrt[1-(0.173648)²] = 1/sqrt(1 – 0.0301537) = 1/sqrt(0.969846) = 1/0.984808 = 1.01543 times as long as the duration of the same event, for the observer, with the event happening at the observer’s location.

Now, if time is taking longer to pass by, then an object’s temporal speed is shrinking, so this slightly longer elapsed time corresponds to a slightly slower temporal speed. As seen in the equations above, near the end of the calculation, the two have a reciprocal relationship, so such an object’s temporal speed would only be 0.984808(temporal c) = 0.984808(60 seconds/minute) = 59.0885 seconds per minute. Therefore, an object moving spatially at 0.173648c would experience time at 0.984808k, where k represents the temporal-only c of exactly 60 seconds per minute — according to Einstein.

Next, to check this against my friend’s “everything moves at c” idea, I need only compare 0.984808 to the cosine of 10º, since, in the diagram above, based on his idea, vector BM = (vector AM)cos(10º). The cosine of 10º = 0.984808, which supports my friend’s hypothesis. It has therefore just passed its first test.

As for the other sets of vectors in the diagram, they provide opportunities for additional testing at specific relativistic spatial velocities, but I’m going to skip ahead to a generalized solution which works for any spatial velocity from zero to c, corresponding to angles in the diagram from zero to ninety degrees. Substituting θ for 10º, the spatial velocity, (c)sin(10º), becomes simply (c)sinθ, which corresponds to a temporal velocity of (c)cosθ, with it then necessary to show that the “cosθ” portion of this expression is equivalent to the reciprocal of 1/sqrt[1 -(sinθ)²],  after the cancellation of c² in the numerator and denominator of the fraction, under the radical, in the denominator of Einstein’s equation for time dilation. By substitution, using the Pythagorean trigonometric identity 1 = (sinθ)² + (cosθ)², rearranged as 1 – (sinθ)² = (cosθ)², the expression 1/sqrt[1 -(sinθ)²] = 1/sqrt[(cosθ)²] = 1/cosθ, the reciprocal of which, is, indeed, cosθ, which is what needed to be shown for a generalized solution.

My friend’s name is James Andrew Lemley. When I started writing this post (after the long process of preparing the diagram), I did not know what result I would get, comparing what logically follows from Andrew’s idea with the well-tested conclusions of Einstein’s time-dilation formula, at even one specific relativistic speed. Andrew, I salute you, and think this this looks quite promising. Based on the calculations above, and after all these years, I must tell you that I now think you are, indeed, correct: in a sense that allows us to better understand spacetime, we are all moving at c.

A Star with 49 Points, to Celebrate the 49-Hour Weekend Caused by the End of Daylight Saving Time, Tomorrow, in Most of the USA


This is the weekend that Daylight Saving Time (or DST) ends in most parts of the USA, which means that this is the only weekend of the year, here, which lasts 49 hours, rather than the usual 48.

To celebrate this once-a-year event, I created the design above, based on the number 49. I started by making one heptagram, inscribed in a circle. The heptagram I used is one of two which exist, and is also called the {7/3} star heptagon. It looks like this:


After making one of these, I then rotated it 1/49th of a full rotation, repeatedly, until I had seven of them inscribed in the circle. Seven times seven, of course, is 49, so this created one type (many are possible) of 49-pointed star. Also, I had already extended the line segments to form lines, so that this geometrical design would extend outside the circle. Next came thickening and blackening these lines, as well as the circle, and re-coloring the red points to be black, as well.

All of this work was performed using Geometer’s Sketchpad. I then took a screenshot, moved the design to MS-Paint, and used that program to add the colors seen in the image at the top of this post.

I don’t like Daylight Saving Time, and never have, but I do enjoy the end of it, when it arrives once each year, and we get our “missing” hour returned to us — the one which was stolen from one of our weekends in the Spring.

To those who live in areas which do not observe DST, such as most of Arizona, you are fortunate — at least in this one respect. Heart attacks actually increase when DST starts each year — a fact which can be easily verified with Google. There are other problems with DST, as well. Daylight Saving Time (one of the worst ideas Benjamin Franklin ever had) should be abolished. Everywhere.

Daylight Saving Time: The One (and Only) Way the Rest of America Should Be More Like Arizona


I’m not used to saying that the rest of America should be more like Arizona . . . but my passionate hatred of Daylight Saving Time forces me to agree with them, when the clock-changes remind me of this fact, twice each year.

Another Modest Proposal (with Apologies to Swift)

The day on this planet is 84,600 seconds long. That’s not far from 100,000 — so we could shorten the second a bit, call it something else, and get 100,000 of them each day to create a decimal clock. 100 of these “jiffies” could make a “stretch,” and then 100 “stretches” could make a deciday (the new version of an hour). Ten decidays, of course, make a day, so these neo-hours are pretty long, compared to the hours we’re used to experiencing. This is just practice for making an improved 10-month calendar, of course.

Why go to all this trouble? To get rid of astrology forever, that’s why!

Time Is Running Out


Time Is Running Out

A lot of people are complacent about the long-term fate of the earth because they know the sun won’t turn into a red giant for >4 billion years. However, we don’t have even half that long to find another place to live. The sun’s luminosity is increasing — so quickly that the oceans will boil away ONLY ~1.5 billion years from now.

Let’s get going with extraterrestrial colonization, people!


[Note: I didn’t create this image, but simply found it with a Google image-search.]

Your Toes Are Younger Than Your Head


Your Toes Are Younger Than Your Head

Unless, like a bat, you sleep upside-down, your toes are younger than your head.


Because, having spent more time slightly closer to the center of the earth, they have endured a slightly stronger gravitational field strength. This, in turn, due to relativistic time dilation, slows time down for your toes, relative to your head. With a slower passage of time during all periods when you were upright, less time has passed for them — and so they are younger.

Image credit: