Robby, who is interested in almost everything

[Robby]

Hi. Formerly Enki, but here I shall be Robby. I was Enki, because I'm fond of ancient Sumerian mythology. Robby approximates the Hebrew pronunciation of "Rabbi". I am a somewhat observant Jew but NOT a rabbi and not orthodox either. [Chances are, I know more about Jewish stuff than lots of folks, but MUCH less than those who have attended yeshiva.] I am an English professor, &, learning of this forum from Randall R. Young, have come here so as to continue enjoying his posts, but to enjoy other intelligent posts, hopefully yours.

I'm very interested in the Hebrew Bible and in other Hebrew, Aramaic and Yiddish texts (e.g., Rashi, Cordovero, Abulafia). Also Eastern lore (Buddhist & Hindu) and mythology, esp. Sumerian, Babylonian,& Greek mythology, and American Indian culture, esp. Hopi but also Navajo, Cherokee, & Sioux. Can't seem to "grok" Egyptian or Norse myths. (As you see, I also like sci fi. Fantasy too, fairy tales, and good kiddy lit. My favorite SF writers incl. Ursula Leguin & Ray Bradbury.) I'm ignorant about music but would like to know more. Also interested in math [please KISS] and in history & bios insofaras they concern what life was like in those days--less in wars, battles, rulers, and dates.

I love good movies & good novels, but I haven't seen any movies for over a year. I like Glenn Close, Michael Douglas, Meryl Streep, Bogie, Kate Hepburn, Jack Lemon, Star Wars, Star Trek, Close Encounters of the Third Kind, Gandhi, African Queen among many others. I missed the king's speech this past winter, alas. I've been reading Daniel Quinn, Daniel Levin, Daniel Silva & Daniel Matt. Also Arthur Green, Michael Cook, David Stern, Gabriel Marcos, Isabel Allende, Alan Morinis, Harold Bloom, Zora Neal Hurston, Toni Morrison, Rudolfo Anaya, Carlos Fuentes, others.

I used to be interested in everything [except bench pressing, football, and motorcycles], but now I am only interested in almost everything.

I dislike earthquakes and wouldn't live in California on a bet. I wish I could visit Japan, but not right now. I've been to Europe once; Egypt once; Peru once to see Machu Pichu and the rain forest; Mexico and Canada a few times each. The major national forests of the western states but not yet Yellowstone, alas. I once flew to Guadelajara specifically to experience a total eclipse. I once took a flying lesson and flew over my own house. I hope someday to visit China and Thailand and Greece and maybe Brazil.

What else? I'm over 60 years old and have changed my ideas about ultimate reality enough since my teens that my teenage self would be aghast. I rarely eat out since hardly any restaurants are kosher. I made the second Seder at my table this year, thank Gd, albeit with only 14 guests, including my two adorable grandbabies, kennenhora. The first Seder was at the home of my cousin, the rabbi. I haven't ridden my bicycle in over a year. What else? I'm unmarried. I love forests, especially the Big Thicket, and hills, esp. the Hill Country west of Austin, and river rafting, and walking along meandering brooks, and camping out. I enjoy medieval and Renaissance painting but am incompetent at appreciating the modern art of the past fifty years or so; however, do very much enjoy Degas, Constable, Turner, Picasso, Modigliani, van Gogh, Gaugin, Matisse, among others; Chagall, who shows the home towns of my grandparents, and of course Cezanne, the master of them all.

Rainstorms are glorious, lightning and thunder more so, and hurricanes are magnificent as long as they don't hurt people--I once walked outdoors in the middle of one, against all advice--but unfortunately there have been some nasty ones in the past five years, hurting Nawlins (New Orleans), Galveston, Houston, etc.

That's not nearly all the stuff that concerns me, but maybe it'll do for starters.

[Chris OConnor]

You get an A+ for that Intro post. Thanks for taking the time to open up and share so many details about who you are as a person. I hope you eventually do make it to Greece. My wife and I spent 10 days in Greece and it was a very rewarding experience on so many levels.

Who is Randall R. Young?

Oh, and welcome to BookTalk.org.

[Robby]

Hi, Chris OConnor.

Well, I'll bet you and your wife had a great time in Greece.

I'd like to find Randall R. Young on this website. He used to be on Amazon but left and said he was coming here. He's good at math--much better than I am--and he said he'd do a deductive proof of the fact that if you add the first n odd numbers, you'd get n squared. I ought to be able to prove it, but I haven't thought of the proof, and I'd like to see his. That's about all I know about him.

How can I search for him and leave him a message? Can you tell me that?

Thank you.

By the way, how can I see the names of all the books being discussed? For example, I've read Huck Finn and have also read Brothers Karamazov (although that one was fifty years ago--Doeskeyevski (sp?) is depressing as heck and I stopped reading him after The Idiot and never did get to the one that everyone reads...I forget what it's called...War and Peace is much cheerier....

Doubtless there are oddles of topics on books I've read at one time or another....

How do I start a topic???

Sorry to sound so abrupt.

Thank you for any help.

And goodnight, Mrs. Calabash, wherever you are.

Do you remember that?

Do you remember Bob Hope?

None of my students recalls Bob Hope.
But they liked his line when he interviewed the first men on the moon. He said to them, "Nobody likes a smart astronaut."

[Randall R. Young]

Great to see you, Enki-cum-Robby!

Well, I promised you a deductive proof, algebraically.

Here is a formula:

n^2 = (n-1)^2 + (2n - 1)

I say it is true for all n. Here's why:

For concreteness, let's say n = 4. So then, 4*4 = 16, and (4-1)(4-1) + (4*2 - 1) = 3*3 + 7.

We note about this result that 3 is one less than 4, which is our starting n. Also that 2n-1 always is an odd number, if n is an integer.

In other words, the square which is 1 smaller has the gnomon (aka "L-shape") which is 2 smaller. Since adding or subtracting a 2 maintains the oddness or evenness (aka "parity") of a number, this will continue to be the case as we reduce n to 0. Likewise, the square one order smaller must always also be square, since it still has the form (m*m). Thus, we can continually subtract 1, until we get to n = 1. Actually, we don't even have to stop at 1, since 0*0 = (-1 * -1 ) + ((0* 2 ) - 1) = 1 + (0 - 1) = 0. In fact, the formula works for any integer at all.

(Giving the gnomon an interpretation for negative squares is a little harder to visualize, though. Algebraically, that doesn't become a problem. )

>>>>>>>>

I called this a deductive proof, loosely. Really, this type of proof should be called "inductive", but 'inductive' doesn't mean the same thing in math jargon as it does in real life. An inductive proof in math means that first, we prove something for n, then we prove it for n+1. Since we haven't specified n, this proves it for every n, automatically--since counting stepwise from n by ones covers every possible n. (The same applies to n-1, since that covers all n as well.)

>>>>>>>>

The cool thing about math is that once we know something by proving it, we really do know it! Now, and forever. These sorts of arguments get settled, once and for all--unlike arguing with the likes of CC or ferengi--wherein NOTHING EVER seems to be settled, except that you KNOW you're going to hit that "ignore" button, eventually.

[Robby]

Thank you for this proof. It certainly seems inductive to me. True, it works downward instead of upward, but does that matter?

Is there a way to create a general expression in "i" or "n" and then square it and find that it works? That would be deductive.

But I couldn't think of a suitable expression.

[Randall R. Young]

Really, it works in both directions. But I presented it going down, so that you'd see it "bottoming out".

I'm not clear what you are saying in the second line, and what that has to do with "deductive".

In math, all proofs are deductive, in that they rely on chains of reasoning and/or logic. The term "induction" in real life has a property (and reputation) of being less than certain, but forming guesses based on experience. There is a joke to explicate this matter, I think, as well as something important about standards of proof:

A physicist, a mathematician, and logician are riding a train together, one day. The physicist looks out the window, and sees a sheep on a hill. He ventures, "I didn't know they had black sheep around these parts, did you?"

The mathematician says, "Correction: 'There exists at least one black sheep around these parts.' "

And the logician says, "On one side."

[Randall R. Young]

I started googling around to see good examples to draw on. I see that the general population (including math teachers) are being taught some unmathematical definitions for induction / deduction. Perhaps I myself am going insane? (I wouldn't be the first!)

But to me, any proof at all relies on laws of logic and reasoning at some level, and is therefore deductive. The steps may or may not be explicitly specified in fine detail, depending upon intended use, audience, and context.

Only some are "inductive", in that they follow my "zipper" format of starting at some n, doing it for n+1, and seeing that this will eventually cover all the numbers/cases.

[Robby]

Randall
Only some are "inductive", in that they follow my "zipper" format of starting at some n, doing it for n+1, and seeing that this will eventually cover all the numbers/cases.

Robby
So you used the classic inductive method.

What about forming an expression in "i" or "n" and squaring it to show that it always works? THAT wuold be deductive!!!

Good one, by the way, about the sheep.

I remember when I first encountered the word "inductive" in a non-math context.

I tried to explain that an inductive proof was indeed valid, going from k to k+1, but nobody could understand what I was talking about. Meanwhile I did not have a clue what THEY meant by inductive.

Did you ever hear the story about the man whose hat was red on one side and blue on the other?

The villagers standing on opposite sides of the road came to blows over whether the hat was red or blue.

And the trickster (for it was he) laughed and confessed what he had done.

[Robert Tulip]

You call that a deductive proof? Here is a deductive proof.

n^2 = (n-1)^2 + (2n-1)
= n^2 -2n +1 + 2n -1
= n^2

2n-1 is the nth odd number, so adding 2n-1 to (n-1)^2 gives n^2.

Therefore "If you add the first n odd numbers, you'd get n squared"

Quod Erat Demonstrandum

eta: And what is more, this mathematical formula is true for all numbers, not just integers, ie even irrational and imaginary ones, except that irrational numbers are never odd. Imaginary numbers can be odd.

[Randall R. Young]

Go for it, Robert!

This is great! (And so concise!)

So, Robby, now do you know how to do algebra? Do you know all about deduction, proof, and the process of mathematical discovery?

If not, we will leave it to Robert's capable hands, who not only knows all this, but also knows the very key to the universe, including the laws of physics and logic God Himself has no choice but to live up to-- since even God Himself could not possibly think up anything Robert himself cannot imagine.

>>>

But seriously, Robert, is this always how you comport yourself? Wouldn't it make more sense if you found out what the topic was? Don't you think we can do algebra, too? (Talk about condescending!)