The Putnam and my big mistake

Found this recently on https://prase.cz/kalva/putnam/putn79.html For the other years, see https://prase.cz/kalva/putnam.html A1. Find the set of positive integers with sum 1979 and maximum possible product. A2. R is the reals. For what real k can we find a continuous function f : R → R such that f(f(x)) = k x9 for all x. A3. an are defined by a1 = α, a2 = β, an+2 = anan+1/(2an - an+1). α, β are chosen so that an+1 ≠ 2an. For what α, β are infinitely many an integral? A4. A and B are disjoint sets of n points in the plane. No three points of A ∪ B are collinear. Can we always label the points of A as A1, A2, ... , An, and the points of B as B1, B2, ... , Bn so that no two of the n segments AiBi intersect? A5. Show that we can find two distinct real roots α, β of x3 - 10x2 + 29x - 25 such that we can find infinitely many positive integers n which can be written as n = [rα] = [sβ] for some integers r, s. A6. Given n reals αi ∈ [0, 1] show that we can find β ∈ [0, 1] such that ∑ 1/|β - αi| ≤ 8n ∑1n 1/(2i - 1). B1. Can we find a line normal to the curves y = cosh x and y = sinh x? B2. Given 0 < α < β, find limλ→0 ( ∫01 (βx + α(1 - x) )λ dx )1/λ. B3. F is a finite field with n elements. n is odd. x2 + bx + c is an irreducible polynomial over F. For how many elements d ∈ F is x2 + bx + c + d irreducible? B4. Find a non-trivial solution of the differential equation F(y) ≡ (3x2 + x - 1)y'' - (9x2 + 9x - 2)y' + (18x + 3)y = 0. The solution of F(y) = 6(6x + 1) such that f(0) = 1, and ( f(-1) - 2)( f(1) - 6) = 1 is y=f(x). Find a relation of the form ( f(-2) - a)( f(2) - b) = c. B5. A convex set S in the plane contains (0, 0) but no other lattice points. The intersections of S with each of the four quadrants have the same area. Show that the area of S is at most 4. B6. zi are complex numbers. Show that |Re[ (z12 + z22 + ... + zn2)1/2 ]| ≤ |Re z1| + |Re z2| + ... + |Re zn|. Out of a possible 120 I scored like 14. That first easy question which should have been a gimme I answered with all 2s and a 3 instead of the obvious all 3s and a 2! Of course, 3**659 * 2 529586439277951893965474092583036590810243522082200596517939604227123416013684342943500654729797215523804442022054078728685938631907140628741647186226659387625833568430667687420250306165230923151125081851800886369853847621855850099589166501531688975135868638057037196353126383349956287985876705820012772736921310134 and 2**988 * 3 7847963431540043854602722527294935135947789148233888726394656164821907112731465740916980313591522398395468795782859962098538661760441753249012141778343682717725513506951341053775201126754666363680142223256625836169615679639208081708373201132380661314383200545180572876704416380604949502078031495168 I think I got like 1 out of 10 points for that problem!

A friend asked me whether I was worried about AI exterminating humanity - thought I would share this

I'm not worried PERSONALLY, but there are some very smart people who are.

Geoffrey Hinton, mentioned in the article, recently left Google because of his concern. He got mentioned quite a bit by Zvi Moshowitz, who puts a "Geoffrey Hinton Watch" on his blog, to which I subscribe.

Eliezer Yudkowsky, of course, makes that the center of his efforts.

And the brilliant Scott Alexander led me to these guys, he was concerned years back...

They might be right that we are only years from the complete doom of the human race, but I am personally less concerned because:

1) I suspect intelligence is overrated

2) Less intelligent people with just a little cunning have been controlling more intelligent people for ages

3) Ramping up AIs is probably going to run into the exponential barriers to calculation that have been plaguing us forever

4) It is going to be hard for even computers to concentrate the allocation of resources by society

5) It is not clear to me that superintelligent computers wouldn't cherish us as pets rather than try to eradicate us. There are a lot of atoms in the universe!

Besides, I think anybody terrified of superintelligent computers is missing the bigger threat of supermanipulative humans. Most methods of PREVENTING superintelligent computers requires SOMEBODY to have an immense amount of power to clamp down on them. I'm more afraid of that SOMEBODY than the uncertain future.

Of all my sausages...

...the only one I still eat regularly is the Todoric.

Hebros Lukanka
Basis: Pork
Hot&Spicy: Not at all
Dominant Flavor: Very meaty
Smokey: Not at all
Verdict:
"Dried Pork Sausage" Another good sausage with an odd shape, at least this does not look like a brain. Pretty much the standard meaty pork sausage.
Worthy

Lasered fighting woman ...

Nope, this is not a B movie.

Quote of the day

"One important detail is that actions that have not yet been tried in a state s are always assumed to lead immediately to the goal with the least possible cost, namely h(s). This optimism under uncertainty encourages the agent to explore new, possibly promising paths.

Artificial Intelligence, A Modern Approach (Russell & Norwig)

Amusing what theory can teach you about how to lead life, and explain its inevitable disappointments. Of course, literature got there first with ""

Knowing Your Sausage 4 -

Slavonski Kulen
Basis: Pork and beef
Hot&Spicy: A bit, nice
Dominant Flavor: Very meaty
Smokey: Moderately
Verdict:
Very good, although the shape makes it a bit suspect for a sausage. It looks more like maybe a brain. An odd, trilobite shape, kind of like 3 fat sausages all merged together. Does not taste at all like real trilobites, though, those are very stony tasting....although the fossilization process might have altered their taste.
Worthy and notable

Knowing your sausage 3

Todoric Volvodianski Kulen
Basis: Pork and beef
Hot&Spicy: Quite
Dominant Flavor: Resembles a spicy pepperoni
Smokey: Mildly
Verdict:
Not bad, but maybe a little too much like pepperoni.
Another sausage where the smoke flavor doesn't really stand out

Knowing your sausage 2

George's Brand Meats, Banijska Kobasica
Basis: Pork
Hot&Spicy: Mildly
Dominant Flavor: Garlic, without a doubt!
Smokey: Mildly
Verdict:

My favorite sausage of this batch (3 varieties, I'll get to the beef sausage soon), but don't try to kiss your significant other any time soon after eating this unless they are made of much sterner, more garlic resistant, stuff than Jocelyn is.
I would not be surprised if "Kobasica" and "Kielbasa" were linguistically related, and indeed.... Wikipedia confirms