What is the Midway Point?

 

Here’s a neat mathematical riddle to use on your friends to prove your genius bona fides. It sounds unsolvable until, well, you hear the solution.

 

Question:

 

What is the exact middle point between zero and infinity?

 

In other words, on this number line from negative infinity to positive infinity, what is the halfway point between zero and positive infinity on the right?

 

Any guesses?

 

Hmm?

 

Seems kinda impossible to figure out, right? At first I thought so, because infinity, that sideways-number-eight, is not really a number, like 3, 17/50, or π^cubed is a number. Yeah, 3 and 17/50 have exact locations on the number line, and even though π^cubed, like pi itself, is not an exactly defined number (it is an irrational number whose decimal expression goes on, it has been proven, forever), it pretty much has an exact location on the number line. But infinity is not a specific number but an idea. A mathematical concept. So it really doesn’t have a location on the number line, except a vague neighborhood that lives ever, ever, ever rightward as you heading that way down the number line.

 

Hint #1 (minor):

 

So the trick is not to think of the question spatially. Not as in the case of 18 inches being the midway point of a yard, or 500 meters the halfway point of a kilometer.

 

Think of numbers themselves, as in types of numbers.

 

Any guesses?

 

Hmm?

 

Hint #2 (major):

 

Every number on the number line can be expressed as a reciprocal. A reciprocal of a number is one-over-that-number. The reciprocal of x is 1/x. The reciprocal of 3 is 1/3. The reciprocal of 17/50 is 50/17. The reciprocal of π^cubed is 1/π^cubed.

 

So what’s the halfway point between zero and infinity?

 

Answer: 1

 

The reciprocal of 1 is 1/1, or 1. 1 is its own reciprocal. But for every single number greater than 1, from 1.0000000000000001 to a googolplex (10 raised to the power of 1 with 100 zeros following it), there is a corresponding reciprocal. Every single one. And that reciprocal is LESS than 1. Every number greater than 1 has a reciprocal less than 1. Therefore, 1 is the midway point between zero and infinity. Not physically, as in a spatial distance sense, but in the number of actual numbers that occupy the intellectual space between 0 and 1 and 1 and infinity.

 

Q.E.D., as they say.

 

Now go and riddle your most intelligent friend.

Fall Comes to Texas

 

With a week of 70-degree day weather – dropping down to the low 50s at night! 

 

But that was last week. Now we’re back in the mid-to-upper 80s. True, that’s about 10 degrees above average for this time of year down here. Still, the leaves are starting to color, and some are even falling. The sky’s dark at 7:30 and the nights are longer, colder, windier. The grass has stopped growing as nature seems to be rummaging through her closet looking for some heavier, more comfortable, clothes to wear.

 

Me, I’m still in the thick of my Kennedy book. I decided to set Clive Barker aside (and that’s a post for later in the week) and have moved on into more existential horror for the season. For music, I’m currently enjoying the tone poems of Richard Strauss on vinyl, an area I’ve always been aware of but never really dug until now. Timing is everything, even in music, I guess.

 

More posts on the horizon …

 

Pagetrotting

 

 

October thus far has been quite the busy month. Aside from the usual ephemera, otherwise known as the daily grind, and other interesting but not blog-appropriate adventures, I have been delving into two thick, hefty worlds of literature, each reminiscent of the adobe bricks found in the Chama Valley of New Mexico. Both laid on a scale would rival the poundage of a newborn.

 

It’s not just the physicality of the two books that are thick, hefty, and brick-like. The subject matter is just as impressive. The word “worlds” used above is not just a metaphor, as each conjures an entire sociosphere and a globe-sized universe of culture, character, and plot. One is of a time now long past, the early 1960s; the other is of a time that’s never been save for within the mind of the author himself.

 

The first book is A Thousand Days: John F. Kennedy in the White House, a 1964-biography-of-sort by Arthur Schlesinger Jr., a liberal historian who served as a Special Assistant to the President during the 1961-1963 Kennedy administration. A darling of and expert in the history of the American left, Schlesinger won a second Pulitzer Prize for this work. Taken with a grain of salt (i.e., one must wear hagiography-repellant glasses when reading), this is a deep immersion into those hectic, heady days of the ’60s prior to what you thought were the hectic, heady days of the ’60s. Back door politicking, the Cold War, Cuba, Khruschev, and a changing culture pushed in large part by the sainted Massachusetts president.

 

The second is Imajica, which I can best describe, for better or worse, as horror maestro Clive Barker’s go at a Lord of the Rings. He conjures up his particular brand of gory, somewhat-occultic fantasy, a journey through five worlds or “dominions” to set free the lands from an evil sorcerer Autarch. There are macabre and freakish races of creatures as a substitute to the well-worn tropes of Elves and Dwarves etc. There’s magic, dreams, societies, and a half-dozen detailed plot lines racing with the characters to the Autarch’s palace. Plus heavy doses of Barker’s subversive sexually-tinged horror.

 

Each has its strong points and weak points. I plan on writing reviews on both upon completion. Each is an investment in time.  A Thousand Days is 1,031 pages and Imajica is 827. With a par of 20 pages a day I should finish the Kennedy book just before the 61st anniversary of his assassination in Dallas. In the past I always read something JFK-related in November, so this is a throwback to that. The pace is doable and I am on schedule. Imajica, however, is more a challenge. It’s this year’s “Halloween” reading, and in order to finish that I need to reach 26.7 pages a day. I am slightly behind schedule at page 390. But I’m up for the challenge.

 

After these two books I think I’m going to spend the last two months of the year deep-diving into Dean R. Koontz. I so enjoyed my retro-reading of Tom Clancy this past March to August that a return to Koontz strikes me as a fun way to end these twelve months. Back from, say, 1989 to 1991, I believe I read 15 of his books. There are five which I’m interested in checking out again: Midnight, The Bad Place, Twilight Eyes, Cold Fire, and Dragon Tears. This might be a bit much for two months, especially with Christmas festivities and all, so it might extend into early 2025. We’ll see. I’m up for the challenge.

 

Anyway, happy readings, all!