The photo here is explained in part by a previous essay, True Meditation . I recommend we click on that before proceeding because I don't know if #2 is going to mesh with it too well. This is because I haven't written #2 yet. As my fellow philosophers and gardeners are fond of saying, lookie!

I had hoped to illustrate this sermon with time-traveling Gypsy wagons and horses instead of bicycles but couldn't seem to draw either today. I like horses very much. One of my favorite movies is "Seabiscuit", which stars Tobey Maguire as a jockey. I don't remember who played Seabiscuit --some excellent character actor-- possibly William Devane, but with the right makeup and vocal inflection he was was very convincing.

So we begin with a graphic depiction that captures only the top half of the word, FRANCE. This means it represents northern France. It shows a lesser known bicycle race to, from, over and around a bright white light that flickers in and out of existence.

There is a black dot in the middle of the light which, if we look very closely, proves not to be a dot at all but a simple algebraic formula:

It says infinity divided by itself equals one. There are accomplished mathematicians who pronounce the equation invalid because infinity is an undefined mathematical value that does not qualify as a rational number. There is a philosophically correct term for proponents of this objection: Crybabies. Although the universe is finite, the emptiness toward which it expands, and does not exist until it gets there, is quite infinite. All possibilities are assembled in it, even mutually exclusive possibilities like my equation and its detractors. That is why we need so much space. Same reason there are more things far away from you than there are right up close. More room out there.

If we grab the universe on the other end, the little end, we observe subatomic building blocks of reality. These are irreducible quanta that become particles or waves depending on what sort of behavior is needed. You get them winking in and out of existence in this continuum as a routine thing. Since, by definition, quanta cannot be further reduced, it follows they are indivisible. They propagate as waves and participate as solids, but how?

Answer must lie with the nature of the universe at large and its mechanical relationship with infinity. That is, infinity functions in constant division of itself, by itself, and all that exists, reality, you, me and some cryptids like the Loch Ness Monster are the quotient --one.

Go in peace.

I should think that the sideboard mural of bicycles which your children made would greatly increase the value of your house. It would particuarly appeal to Lance Armstrong, who - I heard - is looking for a new home where he can exist incognito

ReplyDelete(yes, I read True Meditation #1).

Your explanation of infinity is profound - and I only had to read it very carefully five times to come to that conclusion.

By the way - we should indeed do some doodling, although I think my doodling days are just about over. (I don't want to alarm anyone with this statement. It has to do with Geo's comment on my current blog post).

Thank you, Jon! I had begun to fear readers thought I'd finally fallen through a hole in my shoe and stepped on my brain. Your doodling days are by no means over. As Thos. Jefferson said, "I am an old man but I am only a young doodler." Or maybe I said that --but if Jefferson didn't say it, it's the only blasted thing he didn't say.

DeleteI'm scared! It's 2:30 am and I actually understood you!

ReplyDelete"They propagate as waves and participate as solids, but how?"

I believe Seabiscuit holds the answer or perhaps my favorite,Secretariat. Red Big after all holds all the records so he might be your go to horse. BUT Mr. Ed on the other hand was the gabby one of the bunch of notable equines so maybe you should ask him???? OMG! It's late and I really need some sleep...

Thank heavens for nightowls! Impressive theory --yes, Secretariat. But we need to consider trotters too. Dan Patch broke 14 world speed records, on this planet alone! Now, of course, you've started the "horse of course" song singing in my head. I shall dream of Mr. Ed.

DeleteThat's not exactly my idea of a perfect dream, but I suppose it'll suffice. Oh my! That song is infectious.

DeleteAwe-some as usual. "Crybabies" made me chortle. "The little end" reminded me of Lilliput and Blefuscu. The cosmologists and the particle physicists, warring over who gets the best toys to play with.

ReplyDeleteYes, Swift's account of the conflict between Little-Endians and Big-Endians works well here. Thanks!

DeleteI think it may be too early for me to understand this...or it may be Topamax brain finally kicking in for good. :(

ReplyDeleteI always questioned why there is an end to the universe. What is on the other side ot the end, then?

Secretariat has always felt like MY horse, because he won the triple crown the year I was born, and Louisville is my home.

General consensus is the universe sprang from a notch in nothing and expands upon that original thrust. It contains a finite amount of matter beyond which is an infinite amount of nothing --sort of like me when I first wake up.

DeleteDear Geo.,

ReplyDeleteI was so glad that I survived a long bummel through Berlin's Ale (!) breweries (together with 2 narrowboat chaps and husband - we came back at 3 a.m) without a headache. Now I saw your split infinitives - eh, no, sorry: divided infinity. Thought about it - fetched the little kettle (we are, to be honest, parents of only one son - though he, of course, is infinitely wonderful) - so no big Loch kettle, and made tea. Looked up the Internet: http://www.philforhumanity.com/Infinity_Divided_by_Infinity.html. Decided it is undecided. Start to meditate (that is not a joke, I do it almost every day. Avoiding the frontal lobe, as good as I can - the Taoist way). Makes me feel better than a formula, as did the starry, starry sky yesterday night, so beautiful and somehow infinite.

Unlike quanta, infinity is infinitely reducible and the starry sky...well it's just beautiful!

DeleteThanks for this update! The only thing I have to add to my reply to the first True Meditation--which concurs with what you and the ancients point out here--is this bit from Carl: http://www.upworthy.com/the-single-most-mind-altering-photograph-humanity-has-ever-taken

ReplyDeleteWillie, the photo taken from so far away by Voyager presents a staggering prospect. We are a scintilla.

DeleteThe concept of infinity..foreverness....neverendingness...so hard to grasp. We are beginning and ending beings....we start/we finish...at least visibly. I like to think our energy goes on into infinity and beyond (is there such a thing?) changed over and over again to the requirements of the evolvement of ....what?

ReplyDeleteI can't imagine anything beyond infinity because we only get one. Two infinities would mess up my arithmetic. As to where we are headed, that's another equation.

Delete'It says infinity divided by itself equals one. There are accomplished mathematicians who pronounce the equation invalid because infinity is an undefined mathematical value that does not qualify as a rational number. There is a philosophically correct term for proponents of this objection: Crybabies.'

ReplyDeleteMm. This was good.

Thanks Suze. There are strong points on all sides of the enigma and I hope we surround it some day.

DeleteI participated in that race the first year they had it. I was almost to the black dot, so close I could reach out and touch it, when Buzz Lightyear, or perhaps it was Sea Biscuit, zoomed past me AND the black dot, causing an explosion of white light that seemed to go on forever and the next thing I knew, everything went black. When I came to, I was lying on the floor next to my chair.

ReplyDeleteNot an uncommon result of undefined arithmetic at high speeds, although several times I was able to pull my pants off over my head before hitting the floor.

DeleteSuze highlighted my favorite part of this post, but the whole darned thing is terrific. A wee bit mind-bending, perhaps, but we all need our minds adjusted from time to time. The concept of infinity is one I've grappled with since the beginning of time... or since the beginning of my time, anyway. (Babyhood exempted, unless of course I simply can't recall my infantile grapplings of that period.) I used to think I was a good student of physics, and then I read physics books by some of the greats. (Like Hawking) Now I know I don't know... or understand... a helluva lot. Best if I stick to the finite, and let infinity take care of itself. It's done quite well without me this far.

ReplyDeleteClassical physics provides a firm basis for exploring new ideas --many of which are complicated by gravity leaking from other continuua into ours. Are we being billed for this? Like many other questions posed by modern science, I'm afraid to ask.

DeleteI am going to have to come back and read this after a good night's rest!

ReplyDeleteGood idea. Me too.

DeleteIrrational numbers make me smile- my understanding of it all is rather wavelike but I much prefer a changeable universe. There's room for hope. Appreciate the insight into dealing with ugly sideboards also :-) x

ReplyDeleteYes, changeable. Martin Buber thought the universe is very reliable because you can get it out over and over again. Hopeful idea indeed.

DeleteSubatomic, what? All those symbols...my husband is a physicist. He'll look at it for me.

ReplyDeleteI'd welcome the input as my calculations are necessarily simplified --an involuntary response to tremendous operations that cannot be exaggerated. Thanks!

Delete