Wednesday, November 5

Das Ei des Columbus


Gabriel Fernandes' puzzle blog entry yesterday on the Logic Egg had me thinking about the Richter original called Ei des Columbus, which came out in 1893 to coincide with the 400th anniversary of Christopher Columbus' rediscovery of the Americas. Unbeknownst to me, Columbus' egg was then already a well-worn idiom in Germany, based on an apocryphal account of Columbus shaming his opponents by coming up with something outside the box. In short, Columbus' discovery is belittled by those present at a get-together who suggest that "any of us" could have found the New World. Columbus asks his detractors to stand an egg on its end, something that they are unable to accomplish. So he shows them how by gently hitting the egg onto the table so that its cracked shell now gives it support. Yes, he implores, any of us can do it.

Here is my transcription (I've shortened any long s occurrences but have left the sharp s as is) of the tale from Friedrich Förster's 1842 Christoph Columbus:

     Wir dürfen den Entdecker der neuen Welt nicht zur zweiten Fahrt dahin abreisen lassen, ohne jenes Gastmahles zu gedenken, bei welchem ein sinnreicher Einfall von ihm Veranlassung zu einem Sprüchworte wurde, welches eine eben so weite Verbreitung erhalten hat, wie sein welthistorischer Name; wer hörte nicht von dem Ei des Columbus? Bei einem Feste, welches der Cardinal Mendoza dem Admiral zu Ehren veranstaltete, hielt er ihm eine große Lobrede wegen der von ihm gemachten Endeckung, welche er den größten Sieg nannte, den jemals der Geist eines einzigen Mannes erfochten habe. Die anwesenden Herren vom Hofe nahmen es übel auf, daß einem Ausländer, noch dazu einem Manne, der nicht ein Mal von nobler Herkunst sei, so große Auszeichnung erwiesen würde. "Mich dünkt", bub einer der königlichen Kammerherren an, "der Weg nach der sogenannten neuen Welt war nicht so schwer zu finden, der Ocean stand überall offen und kein Spanischer Seefahrer würde den Weg verfehlt haben." Mit vornehmem Gelächter, hinter welches sich so gern die Dummheit verbirgt, gab die Gesellschaft dieser Aeußerung ihren Beifall zu erkennen und mehrere Stimmem riefen: "o, das hätte ein Jeder von uns gekonnt!"
     "Ich bin weit entfernt", entgegnete Columbus, "mir etwas als Ruhm anzumaßen, was ich nur einer gnädigen Fügung des Himmels zuschreiben darf; indessen kommt es doch bei vielen Dingen in der Welt, welche uns leicht auszuführen scheinen, oft nur darauf an, daß sie ein Anderer uns vormacht. Dürft’ ich", sagte Columbus zu jenem Kammerherrn gewendet, "Ew. Excellenz wohl ersuchen, dies Ei — er hatte sich von einem Diener ein Hühnerei bringen lassen — so auf die Spitze zu stellen, daß es nicht umfällt?" Die Excellenz versuchte von der einen, wie von der anderen Seite vergeblich, daß Ei zum Stehen zu bringen. Der Nachbar hat es sich aus, es gelang ihm eben so wenig; nun drängten sich die Anderen dazu, ein jeder wollte den Preis gewinnen, allein weder mit Eifer noch mit Ruhe war es möglich, das Kunststück auszuführen. "Es ist unmöglich!" riefen die Hidalgos, "Ihr verlangt Unausführbares!" — "Und doch", sagte Columbus, "werden diese Herren sogleich sagen: das kann ein Jeder von uns auch!" Jetzt nahm er das Ei, und setzte es mit einem leichten Schlag auf den Tisch, so daß es auf der eingedrückten Schale fest stand. — "Ja! das kann ein Jeder von uns!" riefen die Hidalgos; seitdem hört man oft sagen, wenn eine glückliche Erfindung gemacht wurde, zu welcher ein jeder sich klug genugt dünkt: "das Ei des Columbus!"

Sunday, October 12

Climb to a prime


I took on my table of A195264 three years ago. I am still chipping away at the currently-317 primary unknowns (out of 10000), extending ECM-factorization attempts from 2000 to 5000 curves. I'm not yet even half-way through the list. Occasionally factordb will have found for me (over time) the large factors for up to 116-digit composites! And in a handful of cases I have evolved an unknown into a prime — which finishes those unknowns from consideration, but there are plenty more.

I've been a little resentful that I hadn't picked the arguably aesthetically-better (one less arithmetic symbol with which to deal), historically better-known home prime sequence (A037274) on which to while away my time. No matter now: John Conway has offered $1000 for a resolution (problem 5) to term #20 of A195264, not term #49 of A037274 — which he could easily have picked instead. I don't believe that (mathematically) it makes any difference: one is as contrived as the other. Conway's point (I think) is that there exist easily-stated but impossible-to-prove conjectures about such sequences. To collect the $1000 for problem 5, you will almost certainly have to luck into a prime in the evolution, because proving that it doesn't evolve into a prime may well be impossible.

While the prize may spur some to further evolve A195265, it may also impede them from sharing any results of that effort. I hope that's not the case.

Friday, October 3

Time has come


My D5300 has a GPS chip in it. I don't own a mobile phone so this is actually my first acquaintance with the capability. Of course I enabled it, even though I suspect that it will be a drain on the camera's battery. As it turns out, only about one in seven of my photos had the location data embedded in it and a cursory look indicated location placement wasn't necessarily all that close. A handful of waypoints had me on the opposite side of the Humber river from where I actually was!

There is an upside. The camera has a set clock from satellite option and I had turned on this feature. The above photo was captured on September 28, exactly 19 days after my first photo taken just after I manually set the camera's clock. The photo's embedded time-stamp was still in sync with real time, indicated here by a website clock. I may never have to correct the camera clock again.

Wednesday, October 1

Shelfie


My new D5300 does some in-camera filter effects. My sense of photography is journalism — not art — so this seems to me extravagant and unnecessary. (If you want to photoshop, use a computer.) Regardless, I tried it out. This "shelfie" is a color sketch effect and its pastel hues are actually quite pleasant. I shared another shelfie on Google+ last year and there is some overlap with this image. The only other effect I have tried so far is HDR painting which was rather disappointing. I had hoped for better HDR and less painting.

Tuesday, September 30

Moving on

Three weeks ago I got a new brain/body for my (camera) lens. I had been using my Nikon D40X with a Nikkor 18-200mm zoom since 25 October 2007, so long enough. The years of use (over 31000 photographs) had baked some dust onto the camera's sensor and these showed up as smudge spots in blue-sky backdrops — very annoying! I suppose this is fixable by a proper in-shop cleaning but the logistics daunted me. So (instead) I purchased a Nikon D5300. It was my intention to take a whole bunch of photos before evaluating the results — but my iMac's two-year-old hard drive died a week into the picture-taking and it took a whole week to replace it. By then, I had decided to upgrade my lens as well. The Nikkor 18-300mm zoom was a near-identical replacement with a small zoom improvement and — more importantly — a lock that prevented the zoom from unfurling under its own weight, something with which I had been struggling all these years.


Monday, September 29

Where the woodbine twineth


My much-photographed island in the Humber, taken on September 20. Usually I'm high up the bank (behind me) looking down but I wanted to see how close I could get to the egret on the rocks (at bottom right). The woodbine in my title refers to the prominent (red) Virginia creeper (Parthenocissus quinquefolia) climbing up a tree.

Wednesday, August 27

What's on first?

A sequence that I'm currently attempting to extend: _, 91, 3854, 178086, 15469622, ... I've purposely left out the surprising first term.

Update: It is now a sequence in the OEIS.

Thursday, August 14

3329 is a prime balanced factorial

It may appear that the following Mathematica execution took just over an hour. In fact, it has taken me many weeks to be able to write it.

PrimeQ[3329!-7607]

True

DateString[]
NextPrime[3329!-7607]
DateString[]

Thu 14 Aug 2014 08:03:36

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Thu 14 Aug 2014 09:12:03

Tuesday, August 5

A beautiful picture

I have suspected for years that the television picture supplied by the evil Canadian Rogers cable empire was sub-optimal at my Toronto house, owing (I thought) to a less-than-perfect infrastructure situation somewhere upstream. It all came to a head three years ago, as this lengthy complaint to an online Rogers employee attempts to explain. A senior technician did subsequently come to the house and declared my television — not their cabling — to be the problem. And alas, that television did indeed suffer from a defect (unbeknownst to me, as the set was borrowed from my daughter) that prevented proper reception on some channels. Rogers charged me $50 for the technician having to come to my house for no good reason, as it were. In light of the defect, I could not press the issue of sub-optimal reception.

Fast-forward to yesterday morning. I had lost my Teksavvy internet signal (which runs on Rogers' cable) and my television picture was somewhat more degraded than usual (so I knew it was an issue with the cable, not the modem). Rogers demands from Teksavvy a full accounting of the situation before they will issue a ticket for a technician to be sent and so I spent a full hour being interviewed by a Teksavvy employee, gathering modem and network details. Subsequently, Catherine found out from our immediate neighbours that they had lost their Rogers television signal altogether.


Early this morning a couple of Rogers subcontractor vehicles appeared and Catherine learned from their drivers that there were additional houses on the street without a Rogers signal. Unable to fix the problem on their own, they issued a Mayday to Rogers. The Rogers truck (pictured) appeared before ten. By noon I had my internet back — although it was off-again/on-again for several hours as they continued (I guess) to troubleshoot the line. Finally, they were done. I had my internet and when I turned on the television — I had a pristine picture the likes of which I had never seen. So yes, I did have a sub-optimal feed all these years!

Tuesday, July 22

Cousins

I thought Kaya and Bodie were step-siblings. Actually, they are cousins. Kaya came for a visit just now. You can see that we've trimmed Bodie's ears and tail.