Happy birthday! If you were born in the year 1940, then this year you are "one degree of precession" old! Some very special people reach that special age this year.
The map above shows the pre-dawn sky, facing east. We can use this illustration to discuss "one degree of precession."
Right now, the pre-dawn sky above the eastern horizon is pretty spectacular, with Orion followed by Sirius beautifully visible, and above Orion the Hyades and the Pleiades. Shifting our gaze along the horizon and going towards the north pole from Sirius and Orion, we will find the majestic Lion (Leo) rising up out of the horizon, barely clearing the horizon before the rising sun engulfs the sky in light and the stars retreat from view until sundown. This year, the brilliant planet Venus is hanging in the sky like a shining jewel just beside the Lion.
For a wider-view diagram than the one above, a diagram which will show the position of Sirius in Canis Major relative to the Lion, see this post from a couple weeks ago. For a post discussing the other beautiful stars and constellations that can be easily located starting from Orion, see this previous post (it discusses those stars in the context of winter, when they rise above the eastern horizon after nightfall, but right now they are rising above the horizon before daybreak, and rising a bit earlier each day, and as they continue doing this in the coming months they be in the above locations earlier and earlier in the night, until they are in the eastern sky in the hours after sunset instead of in the hours after midnight).
Below is the same image as the one above (both from the very helpful and free Interactive Sky Chart tool from Sky & Telescope). I have drawn in the lines for the zodiac constellations Leo and Cancer and marked the bright stars Regulus (in Leo, his forepaw), and Procyon (in Canis Minor), as well as the planet Venus.
Now, if you were born at this time of year in the year 1940, and if you carefully observed the sky every year on the exact same day and the exact same time and used the exact same observation point each year, and you started the day you were born (I know -- infants cannot really focus on stars the day that they are born, but this is an illustration for the sake of discussion), then you would notice by the year 2012 (after 72 consecutive years of such observations on the exact same day each year) that the stars were ever-so-slightly "behind" their anticipated locations at the chosen day and time.
Of course, you would have to be very precise to even notice the difference after 72 years of annual observations, because the difference would only be one degree of elevation after all that time. To understand what one degree means, simply remember that the entire sky turns 360 degrees to make a full circle, and so if you have a perfectly flat horizon it is ninety degrees from the horizon to the zenith point directly above your head, and then another ninety degrees back to the opposite horizon. So, one degree is what you get if you divide the entire 180-degree arc from one horizon up through the zenith and back down to the other side into 180 equal segments (or if you divide the arc from the horizon up to the zenith into ninety equal segments).
The helpful diagrams from Sky & Telescope usually contain a degree scale for ease of reference. In the diagram above, the right-hand edge contains marks at elevations of twelve degrees and twenty-four degrees. I have added a white-and-purple "degree scale" with twenty-four degrees on it (twelve of them white and twelve of them purple, alternating) so that you can see what one degree looks like.
Also, you can estimate a degree by extending your arm fully out in front of you and raising your index finger -- the width of an index finger viewed at arm's length covers about one degree (you will have to hold it parallel to the horizon to see one degree of elevation using the width of the finger). Because of the way our fingers fit together and their different widths, if you raise three fingers beside one another (your index finger, middle finger, and ring finger) and hold them at arm's length, that will cover about five degrees of arc.
Knowing all of this, we can now direct our attention to the diagram below, which is identical to the one above but which includes an additional "degree scale" closer to Leo, and shows about how much difference there would be between the observed location of the star Regulus on this same day and time 72 years ago and the observed location of Regulus today. Because of the action of precession, Regulus has been "delayed" one degree and is now one "purple bar" below where the star would have been on the same day at the exact same time and observed from the exact same location in 1940.
For simplicity, the above diagram only shows the difference in the location of Regulus -- but in fact all the other stars have been similarly "delayed" by precession, such that the entire constellation of Leo from this day in 1940 would be a bit "higher" than he is in the outlined diagram above, and Cancer would be shifted by the same one degree as well, and so on.
Note that we are not talking about movement of Regulus (and the other stars) from one night to another throughout the year -- we are talking about the movement of the star from its expected location on one singular day from one year to the next. If you could measure the elevation of a star when earth is at the exact same point in its orbit from one year to the next (and that is not easy unless you have a very precise calendar, with leap years, or unless you have a very precise way of measuring the exact date of the solstices and/or the equinoxes or, as Professor Gordon Freeman points out, the "Equalday/nights"), you would expect to find the star at its same location once per year when observing it from the exact same point in earth's orbit.
If Regulus is eight degrees above the horizon at exactly 4am on September 23, you would expect it to be eight degrees above the horizon again at exactly 4am on September 23 the following year. Each day of the year it will be at a different elevation on consecutive days (roughly four degrees ahead of where it was the previous day), but by the time you got back to the same day and time one year later it should be right back where it was the previous year. However, due to the extremely subtle action of precession, it will be delayed an imperceptible amount each year, adding up to 1 degree of delay after 71.6 years.
That means that if you are turning 72 this year, and you observed and took careful measurements on the same day, hour, and location year after year starting the year you were born, you would be able to measure one degree of precession between 1940 and 2012.
Let's just take a moment to let the difficulty of measuring precession sink in. It assumes long years of careful observation. It assumes the ability to measure precisely the elevation of selected stars, and then to record those measurements. It assumes the ability to measure from the exact same location on the globe from one year to the next for all those long years. It assumes the ability to accurately understand when the earth is back at the exact same spot in its orbit from one year to the next, in order to take the measurements. Then it assumes the ability to notice the differences after many years and perceive what is going on.
Conventional history (acknowledging the difficulty of making such observations, keeping such records, and analyzing such subtle differences) asserts that mankind did not perceive this phenomenon until Hipparchus (c. 190 BC - c. 120 BC). However, there is very clear evidence which makes this assertion very difficult to swallow -- one of the clearest pieces of evidence being the ancient Egyptian myths involving Osiris and Set, which obviously encode knowledge of precession (and which are clearly very ancient, with references to Osiris and Set and Horus and Isis, who are all part of the precessional aspects of the Osiris myth, found in some of the very earliest extant texts we know of from ancient Egypt, such as the Pyramid Texts of Unas from the period 2375 BC to 2345 BC).
So, if you were born in 1940, happy birthday! It is a great time of year to observe the rising stars before the dawn, and to contemplate the subtle celestial mechanics of precession, and the amazing fact that human beings contemplated it as well, over 4,300 years ago.