Da Vinci Days
Oregonians for Rationality booth

Martin Gardner's Buzz Saw
A  puzzle about cutting cubes

A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes.  He can do this job easily by making six cuts through the cube, keeping the pieces together in the cube shape.  Can he reduce the number of necessary cuts by rearranging the pieces after each cut?  Either show how or prove that it's impossible.

A set of 27 small cubes was provided to let puzzle solvers try out different rearrangements after each pass of the saw.  Here we see the first slab cut off and then placed to take advantage of the second cut so that it will make a bit more of the needed cuts.

You will understand this principle better if you have at least tried to solve the puzzle before reading past here:

Another puzzle, "MAKE A CUBE" also conveyed this information:

"This puzzle has almost no secret at all.

It was simply to arrange 27 small cubes to make a larger cube that had all the same color on the outside (red or blue), and had all the inside surfaces white.

It does have a little bit of a secret...see below.

Here it is assembled:
The solution to the buzz saw puzzle is revealed by the center cube of this puzzle.  All its surfaces are white (the only one with all white surfaces).  All the white surfaces in the puzzle must be created by a fresh saw cut in the other puzzle.  All six cuts of the center cube must be made: five-cut (or fewer) solutions are impossible.
Before you see the answer to this puzzle, a five-cut solution seems at least a possibility.  But...
When you see the solution it's not a guess.
It's a certainty in a very special way.
Nobody can show you it's wrong.
If anybody tries, you know they don't understand the answer.

"Buzz-saw certainty"

Much of science is made up of concepts that have many points of Buzz-saw certainty.
Yet, these points often go "unseen," and the certainty is not recognized by many (most) learners of science.
A pseudoscientific idea is usually made up of concepts that have many "five-cut buzz-saw" elements.
Real science goes simply unseen, awaiting the hard work that leads to those buzz-saw certain insights.

Now, suppose someone has offered a $3000 reward for anyone who demonstrates a five-cut solution.  That’s a pretty good incentive to believe you have found that solution.  And there’s someone who claims to have done it.  He is certain he has.  The person offering the reward is just as certain he has not.

One opinion is wishful thinking.   One opinion is logically correct (more than “just opinion”).

Self-deception      vs    "She (Mother Nature) who must be obeyed"

Always look again!
There's more than meets the eye.
and more, and more, and more, and...

Everyone can see some thing(s) that someone else cannot.

It might be a perception

......The three dimensions of "normal" color    The two dimensions of protanopia.

If your color vision is "normal" you see a difference between orange and grass green.   But a person who is "protanopic" sees them as being the same color (that person has no red-sensitive detectors in the eye).

It might be something from the "fourth-level of abstraction" (the abstractness of math and of James Joyce's Ulysses, e.g.). You might see the ordering of "normal" human colors as fitting properly into a space of three dimensions, while the protanopic colors fit into a space of two dimensions.  Only a small percentage of people understand this abstraction well enough to see how it applies to, say, bird color, which has four, five, or six dimensions to its space.
It might be something from elementary math:
Jerry Manheim tells this story from his course in Diff. Eqn:
I asked him to help me work through a problem (since I firmly believe Math is not a spectator sport).  No matter what question I asked he was silent. 
"Finally, in desperation, I said: "Look, this is basically subtraction;  what if the temp is 4 degrees F outside (O.K., so it 's never 4  degrees in CA....pretend you're in Alaska), and then the temperature drops 7 degrees, what is the new temperature? 
I decided to wait him out on this one and eventually he told me that the temperature is now zero. 
B's and C's in  College Alg, Calc and Analyt (3 terms) and doesn't know about neg numbers.  Who in  hell's name are we doing a favor for....surely not this ELECTRICAL ENGINEERING student.
We need to see the pattern of pattern which is shared by points on a line and Jerry's simple addition of a negative number to a positive number.  From there it's a short step, almost never taken, to see how our idea of measurement is almost always a gross oversimplification.
It might be from elementary physics:  "Energy is the capacity to do work."  "Energy can be unavailable for doing work."  Some people see a contradiction here; some don't.  The error of that definition for energy has the same logical error made if we define "vegetable" with "A vegetable is a potato."  About half of elementary physics textbook authors make this error of elementary logic.

This logical error has a pattern of pattern in common with the error usually made by people trying to solve a well-known logic puzzle that was studied by Percy C. Wason.  IQ seems to measure something that leaves out his important aspect of intellect.—a person who fails to see this pattern may boast a very high IQ.  SEE

It might be from philosophy: We have watched some of the "Post-Modern" academic philosophers take extreme positions which proclaim that we construct reality in our brains with nothing "out there" in the "real" world that corresponds to "our own individual reality."

From our viewpoint, they are also denying modern science, its methods, its insights, its usefulness in making things happen the ways we want.  We suggest that they deny its insights because they simply don't "see" those patterns of patterns in nature which science sees.  They cannot then use those modern, powerful human tools for making things happen the way we want. LOOK HERE.

When we don't see one of the patterns of deeper reality,  we can easily convince ourselves it simply doesn't exist.
It's then we should  ponder those patterns we didn't see or susspect until, one lucky day
while we were thinking hard about some problem, it suddenly hit us:


Everyone can see more things, if they're willing to work at it.


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Da Vinci Days, 2002

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