George Rebane

OK boys and girls, it’s time to take a break from our socio-political harangues and debates, and delve into something more intellectual yet delightfully accessible.  The figure contains a 10-by-10 network of nodes each identified by their blue numbers from 1 to 100.  The related red numbers denote the cost of traversing that node.

The problem to be solved is to identify the minimum cost path between a given starting node and a destination node.  Here, let’s arbitrarily say we wanted to start on node 19 and end on node 92.  What is the path or sequence of nodes to be traversed that minimizes the total cost of the trip when all the costs of the visited nodes are added up?  And as you puzzle on the solution, see if you can come up with an algorithm that can solve all such problems.

The rule for traversing is that allowable steps for any given node are the eight or fewer  of its neighboring nodes.  For example, from node 25 you can step to nodes 14, 24, 34, 15, 35, 16, 26, 36; and from node 31 you can step to 21, 41, 22, 32, 42.

This is a simplified yet still powerful version of a problem that I had to solve long ago on a contract to develop an interactive combat system for combined arms field operations.  The specific problem was to compute and display a minimum time feasible path across a region of complex terrains for a given make-up and size of a combat unit to get from their current location(s) to a selected location.  Today a version of the resulting algorithm is used in you car’s and cell phone’s route calculating apps.  Have fun and let us know your solution and algo.

George Rebane

[This 23jun25 blog post was mysteriously deleted by Typepad which they cannot recover.  I fished out a partial draft version of the post from the Recycle Bin and am reposting it here.  It does not include the two updates and graphics of the original of which I don’t have copies.]

Don’t let an unknown perfect be the enemy of the known good.

At this writing (23jun25 1300) Iran has impotently attacked US bases in Qatar and Iraq in response to Midnight Hammer.  Team Trump is huddling in the White House with his national security mavens to determine what the appropriate follow-on attacks might now be carried out on Iran’s energy and transport infrastructure.  It is clear that the country’s raghead rulers are desperate and properly scared.  Apparently they are convinced that any further diplomatic efforts sans a military response will assuredly result in regime change with their individual heads on the block.  They can easily picture their lifeless bodies dangling from construction cranes in Tehran.  Their alternative is to buy time with some attacks on our regional assets that may cause a US response to sway worldwide sentiments in their favor – e.g. Putin’s call for unconditional cease fire.

Since the B-2s flew, what I’ve found interesting, but not unexpected, are the responses by those who think that Midnight Hammer was unlawful and/or a mistake to insert the US into the Israeli/Iran war.  And here I’m referring only to those who do believe that Iran should not be able to develop or possess nuclear weapons, and has now been in the process of such development for years.  Those who do not believe that Iran is well on its way to having a deliverable nuclear bomb are not worth wasting time with.

The remainder of Midnight Hammer critics gather under the beliefs that 1) diplomacy would work and should be given another chance, and/or 2) this was not the right time nor the best way to take out Iran’s nuclear facilities.  When I ask them on what evidence do they pin their hopes on diplomacy, they can cite none but only repeat the hope that this would work and Iran would verifiably destroy its nuclear development capacity and surrender its 60+% uranium stores.  All the deep thinkers in this group ignore both recent history, experience, and the commonly accepted definition of insanity.  They simply remain wrapped in their comforting blind faith.

The second group simply asserts their gut feel.  These consist of those who believe that Midnight Hammer was a faulty response and/or badly timed.  When pressed for the evidence that supports those assertions, they come up empty.  They cannot recommend a better way nor a better time for taking out Iran’s nuclear capability.  They can present no better set of alternatives simply because they can neither list them nor present any evidence why a possible Plan B would have been better to serve American and Israeli security interests.  They simply reiterate their strong gut feel and hold that up as their gold standard for reasoning about such geo-strategic matters.

A lot of the world debates under such frayed principles, always generating much heat and little light in the process.  I was trained in professions that required critics of Plan A to come ready to also present a Plan B along with its reasonable basis.

[Where is the eternal debate going on politicians lying?  It seems that our leftwing readers gleefully highlight every Trump pronouncement that is in any, even minute, way flawed as an intended lie.  But they totally ignore the daily pronouncements of Democrats as members of the greatest perennial lying machine in the country. gjr]