Prequel to Sequel to The nature of proofs

While a proof of some claim A need not be shown in order for it to exist---a "constructive" proof game for A may be inverted to a dual "classical" proof game for not(not(A))---such a game makes sense only if every refutation R₁ of a refutation R₂ of A can convince the adversary that R₂ is indeed invalid. More specifically, the underlying logic cannot be inconsistent; the claim A must be expressed in a logic that does not allow the player to refute not(A) once a correct proof of not(A) is shown by the adversary.

Sequel to The nature of proofs

A while back, I ranted on when a proof may hope to be correct---the import: only when its construction and verification are essentially devoid of any intuitive understanding; you need intuition only to understand a jump in reasoning, which does not a correct proof make.

However a proof need not be shown in order for it to exist.

Formal theorem provers like me always kind of look down on the lesser mortals who talk about statements and their "proofs" in English. Even when the statements can be formalized, the "proofs" can seldom be interpreted in any coherent logical framework as sound representations of arguments for their truth. I argue that there is in fact an interpretation by doing lesser, that is, by not offering a proof at all.

In intuitionistic logic, all proofs are constructive, that is, a statement is true only if there is a proof that can be shown for it. In classical logic, however, a statement is true also if there is no proof that can be shown for the contrary. A similar idea appears in mathematics under the veil of the Axiom of Choice. Essentially, it can be proved that something exists without actually showing what it is. This is as much a theory as anything else---the Axiom of Choice follows from or breaks a number of mathematical results.

The point of the argument is that classical logic, to be fair, is as good a framework to judge "proofs" as intuitionistic logic. That out of the way, now consider the following (very common) fix:

I say that statement P is true, but obstinately refuse to show you a proof for it. What can you do about it?

So. Normally, if I say that a statement is true, it is my obligation to prove it. In this fix, it is your obligation to disprove it. If the statement is indeed true, you can never disprove it. Hence I "prove" that my statement is true by staying quiet and confident.

A possible fallacy is that there is no way to verify this proof. I could write up a complete strategy to break any argument you might offer to disprove my statement; this might constitute a "proof"---in logical terms, it is a proof of not(not(P)) instead of P; in other words, it is a proof that shows that it is absurd that P is absurd. However, if it is agreed that I am not the defender, that you are the prosecutor, then I should be okay to hide my strategy. Heck, to not even have one, or come up with one on the fly. All I need is to ridicule you whenever you say something that I have already dismissed as ridiculous.

Point made? I'd better not say too much. I probably would have done a better job by not making an argument.

Magnetisms

My advisor left an office-magnetic-poetry kit in the lab the other day. My labmate had the first go the very same evening:

our.vision.is.to.monkey.with.technology.solution-s

And then last evening I suddenly saw too many fun ways to use some the remaining words. So I squatted on the ground and filled up a section of a drawer with random samplings, rearranging them to sound like English (and on the way, have them seem to dig obscure references to the office couture we're used to, maybe?):

I.come..eat.lunch..take.a.robust.nap
know.when.to.think.serious-ly
please.crash.me.young
I.can.maximize.sound
how.did.this.paradigm.shift.while.you.were.here
let.us.build.a.new.problem.together
we.must.meet.under.the.desk
never.communicate.on.my.machine
time.will.make.the.future
full-y.dress-ed.smart.women.always.get.some.sex.at.my.cubicle

So quietly

A crowd of friends are sleeping over at my place tonight. The chandelier burns at the faintest dim above darkness. G breathes peacefully on the left; he has taken it upon himself to wake us up at a quarter to seven in the morning. S snores, restlessly tossing over every now and then on the couch; perhaps he dreams of the girl he was for a good part of an hour on the phone with a while ago. I belch up the smooth aftertaste of peppered pesto. And Svo Hljótt whispers down my eardrums.

Delight

"... forrrty sevenn...forty eight... forrty neine- *big man with pony tail and specs, dressed in jeans, rattles off in a placating grown..*

"... fifffty... fiffty onne... hey, you know who's fifty one? You know? Well Nanny is, Nanny's fifty one!"

"But I don't want to-" *whines a three-year-old girl sitting opposite the coffee table*

"But you have to, dear. We are playing a little game here, aren't we? We are seeing if we can count till hundred, and whether Anne can-"

"But I donnnnnnnnnnn't want to-"

"But it's fun, Anne. Now where was I? Daddy lost count... can you tell me what number we were at? Anne? Okay, let's start over again-
"Onnee... twooo... thurree... foourr... faaaive..."

*some time passes by, as I'm lost in thought... the next time I hear them-*

"You missing Nanny? No-nonono-... you need to hold the drink with both hands, okay? Like theeeesss... there you go! Hey, isn't this brownie yummy? So yummy in the tummy..."

"But I DONNN'T WANT TOOOOO-"

Allergic

Hidy tidy, Christ Almighty,
Who the Hell are We?
Zimm Zamm! God-damn!
The Mighty Vindies We!

Vindy-Hoo Vindy-Hah!
Vindy-Hoo! Vindy-Hah!!
Vindy-Hoo!! Vindy-Hah!!!
Vindy-Hoo!!! Vindy-Hah!!!!

Nostalgic

Here.. boys, lets-sing a school song
For the best schoooool of them all..
Cheer.. boys, cheer-for St. Patrick’s,
Cheer-for St.Patrick’s Asansol..

Whatever-the-task, on us, depend,
We’ll-fight-to-the-last, our school to defend,
Whether-at books or games, it’s all the same,
We are always top in the end. [PUM PUM
PUH]-

(So) here.. boys, lets-sing a school song
For the best schoohoooool of them all...
Cheer.. boys, cheer for St. Patrick’s,
For-we-are-the beeesssstttt ooooffff aaalllll!

Touch

3:15 am. I raid the fridge, stealing another piece of chicken, and munch in thought. I look at the tortilla rounds, think a bit more, then walk back to my bed, get the plate I'd left there after dinner, grab a handful of them chips, dab in a decent amount of salsa, and walk back to my bed with the plate. Thinking, thinking.

3:21 am. New mail. About work finished earlier in the evening. I want to start something fresh in the morning. No worries about lunch tomorrow!...biryani in the fridge, that's the chicken I snicked.

3:43 am. Now.
This, as usual. A new post tonight. I travel from there thence, beyond and back. I've been doing this all week. I love the reads. A couple of mornings back I mentioned this blog to my girlfriend. I can often tell by her voice when she does not like something, and especially when it's me talking about another girl, which she never likes (and don't I adore that!)---the fact that this girl's name is pretty close to hers does not help. What I did want to tell her about this girl is, well, irrelevant. What she said to that, and what I think of it today, are therefore and otherwise, of course, again, irrelevant.

Alright, so this girl is a mystery. I've been reading about her, her grandmothers, suitors, flatterers, a lot of others she points to. Quite unknown to her, she entertains me everytime I type 'm' on the browser URL box, wait for the autofill to do its thing, and enter. It is funny to imagine I'm writing about this, and it is even funnier that I do not want her to know about it. She writes really well. She's funny. I'm sure I couldn't keep up with in real life. Yet safe behind the bush, I love reading her write and can't help but smile.

...

It rained like crazy all weekend. It never stopped raining. No, mister, when I say it never stopped raining, I mean never, never, yes, that is to say, it rained all the time. Pitter-patter-pitttter-patter, howl howl howl. Oh-and-did-I-mention, I went to see the chimp last night, chimp, ape, pot-a-to, pot/a/to, whatever, was a nice watch. Here's the report: tried the "Before Sunset" shave, dressed in black, microwaved the cappuccino from the night before (oh-and-was-that another story! I could not, could NOT for my life let myself drown into sleep that night, so I went out at six in the dark morning to get that coffee---and stupid me, felt really sleepy before I could finish half of it, so)...now-where-was-I?Ah-so, dressed in black, armed with a huge black umbrella, I set out to see the chimp. Was a twenty minute walk, was feeling cheerfully lonely, I'm always cheerfully lonely when I walk briskly and the air is cold. Not many people were out with umbrellas, and believe me, there were many people that evening, out enjoying the rain, and I thought to myself, fuck it, put this huge black thing away that's giving you the aristocratic-buffoon-in-the-age-of-poverty look, so I apologetically went umbrellaless the few more hundreds of steps to le théâtre. It was crowded, it was fun, the chimp was good entertainment. I walked back whistling, stopping for some hot chocolate at a certain cookie place on the way whose hot chocolate SomebodyIknow raves about, nodding in disapproval after taking a couple of sips, which thence added that accidental tune to my whistling.

(I would like to admit here and now that I cannot whistle anything, that I pretend to whistle but all I can do is the Oh Baby one or that Wow Baby one, both tools of the average streetside Romeo that I never was, and that nodding vigorously is the only way I can get the semblance of a wave riding on the monotonous drone.)

It was then that it happened.