HEAVEN PALLID TETHER 1 REPEAT RECESS DESERT 3 MEMORY CELERY ABCESS 1

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1 Heard of "the scientific method"? There's a really great way to teach (or learn) what this is, by actually DOING it with a very fun game -- (rather than reciting the standard sequence of the steps involved). This game crystallizes the essence of the scientific method, as we'll go over shortly. One fairly well-known version of this game is called "Mastermind" -- which involves sets of colored pegs in an abstract color pattern that your opponent tries to find out from clues you give in response to guesses s/he makes. The version we'll talk about here, though, involves words; a five-letter variant is known as "Jotto", but we'll work with a six-letter version, simply calling it "the six-letter word game". You and your opponent each have a secret word, which the other person tries to find out in as few "shots" as possible (less shots than the other person takes for your word that s/he has to find out). For our purposes here, we can ignore the competitive aspect and just concentrate on the process of finding out the "target" word that the other person has. Each "shot" you make is a sixletter word, a guess about what the target word is. The other player responds with nothing but a NUMBER: the number of "hits", or matches between the letters in the word you shot with the same letters in the same positions in the secret target word you're trying to figure out. That is, for how many (if any) of the six letters in the word you just shot, would you find the same letter, in the same position, in the target word? For example: Let's say the target word happens to be "CHURCH". If the word you just shot is "THRUST", then the other player should have responded to that shot by saying "1". (The "H" in the second letter position matches that first "H" in "CHURCH" -- but there are no other matches in this shot.) If you had shot "CRUNCH", though, the reply would have been "4" -- as illustrated with the text format here. And what if you shoot "PATCHY"? Even though there is an "H" in that word, too, (as well as a "C", for that matter), the response will be "0", because none of the six positions have the same letter in both the target and the shot. (Seems to me that there's also a bit of similarity between this game and the good old game of "Battleship" -- where you're trying to "hit" loaded squares that are hidden in some abstract patterns on graph paper?)

2 I've found that even students who aren't at all interested in whatever they're supposed to be learning in some science or math class LOVE this game! I'll split up the students into groups (of maybe four or five, with a large class), and have them take turns bringing me their next shot -- and I tell them how many hits they got, and then they go back to more sleuthing with the clues they've thus accumulated. In order to avoid the undesirable circumstance where one team gets lucky and happens to get a hit or two right away, while the other teams take a lot of shots before getting any hits, I start everybody off with some hints -- say, three sample shots that apply to the target word I have in mind, where one of the sample shots has no hits, one has one hit, and one has two. That way the whole class is on the same footing, with some initial good information to start working with right away. (I've now written a little computer program which anybody can use to play this game, at leisure. The students in a class no longer need to come up to me every time to get the report on the number of hits in their latest shot.) Here's a "sample run", a set of shots I made in a recent game, along with the corresponding reported numbers of hits. On my very next shot I got the whole word -- so the reply from the other player was "6"! See if you can figure out the secret target word, given this information. (If you don't come up with it -- or want to check your answer -- look at the fourth word on the 17 th line on page 253 in this book!)... NOTE that sometimes you can fool yourself into thinking you're getting the same hit with lots of shots, when actually you're getting a bunch of new hits, all over the place. That may be the case, in this following set of shots!...note also that a "ZERO" does not mean you wasted a shot; it's usually very useful information that helps you rule out bogus possibilities! HEAVEN PALLID 1 0 TETHER 1 REPEAT RECESS 3 2 DESERT 3 MEMORY CELERY 2 3 ABCESS 1

3 LEPERS 2 DESIRE FELONY 1 2 HERESY 2 DOCENT 3 6! ***** So, what the heck does this have to do with scientific method? EVERYTHING! I maintain that this is almost PERFECTLY ANALOGOUS to the scientific method! What's the standard rap on the scientific method? You're trying to figure out something about how the world works, and you start with observations of phenomena out there. You notice some patterns, and begin to develop a theory, or hypothesis, about the way things work. So then you can test that hypothesis by seeing if something that should happen -- IF your hypothesis is TRUE -- does actually happen when you try it out with an appropriate experiment. If it turns out that your observations from the experiment VERIFY the prediction you made from the implications of your hypothesis, then you've got a little more evidence that you're on the right track. But if your experimental results go AGAINST the implications of your theory, then it's back to the drawing board, and you need to develop some alternate hypothesis. Well, think about it -- this is exactly the process going on in our six-letter word game! The secret target word in your opponent's mind is analogous to the secret of nature that you're trying to divine with the scientific method. You make some observations -- shoot a few words -- and from the reported numbers of hits (the experimental "data"), you pick up on some patterns, and begin to get an idea (a hypothesis) about what letters might be in certain positions (what the structure of nature is!). Say, you think for sure that the second letter must be an "E" in the target word. OK, so you shoot "SETTLE". If you hear back "0", then you immediately know you were wrong -- but that's important information! You've just falsified that former working hypothesis -- unburdened yourself of a worthless idea! But if you hear back "1", (or even some higher number), would that prove you right? NO! -- The hit(s) you got

4 might well have been among the OTHER letters in "SETTLE" (unless you've already accumulated enough other information to rule out every single one of the other letters / positions in that word). So eventually -- with an efficient, smart sequence of shots, or experiments -- using both observation and logical analysis, you can home in on what that secret word (or secret of nature) is -- same as with science! There have been times in the history of science when major revolutions in knowledge occurred; and such occasions also tended to be painful realizations that (as Cheech and Chong said) "everything you know is wrong"! Whole edifices of "knowledge" had been built up on what turned out to be bogus assumptions about the way things work! Sometimes all it takes is one little counter-example, contradicting the implications of your theory, to force you to throw out the whole thing! ( ~ classic -- Merc. perih. prec.... ) Scientists, being human, sometimes resist evidence that they're wrong -- and don't tend to like having to go back to square one after having invested tons of time and mental work on some pet theory! If you play this six-letter word game enough, you'll see the same kinds of things at work there. A hit where you expect one (or, sometimes even more seductively, a few repeated hits in the same position, with all your different word shots so far) can be consistent with your theory, yet not prove it correct. All it takes is the lack of a hit, where you were expecting one, to make you re-think your hypothesis. In science, we never really prove any theory; we can only disprove things, by logical contradiction. Even the idea that gravity is going to cause a pencil to fall if I let go of it (while standing on the surface of the earth -- not in an orbiting spacecraft!), is still only a theory! That theory certainly has TONS OF EVIDENCE by now to SUPPORT it -- but all it would take is one time that somebody lets go of a pencil and it DOESN'T FALL, to precipitate a major revolution in science -- which would be huge progress, even if for some scientists who were attached to that theory, it's a real pain in the ass!... And this is why there's such impotence in that catch phrase so often used by the people who FEAR the concept of EVOLUTION: "It's only a theory". Hell, even GRAVITY

5 is "only a theory"! (And I think even those people would support the teaching of gravity in our schools!) One difference between the word game and the scientific method is that when you finally figure out the word, you've proved all your hypotheses about it, once and for all -- whereas in science, things usually keep coming up from time to time, showing deeper and deeper layers in the structure of the natural world. Theories eventually have to be refined, or even fundamentally revamped, to incorporate new observations of reality. You have to stay YOUNG (at heart, anyway) and FLEXIBLE, to ROLL WITH THE PUNCHES that science delivers with new data. If one were to summarize the main characteristic of the scientific enterprise in just ONE WORD, that word would have to be HONESTY. That applies not only to the way you come to your conclusions, but also to the way you do your LOOKING: EXPLORATION and OBSERVATION (not hesitating to ASK QUESTIONS whose answers may prove you wrong) -- and it's really what science is all about. Observe the world as objectively as is humanly possible, and then just be RUTHLESSLY HONEST about what you find out. CALL 'EM AS YOU SEE 'EM (to borrow a phrase from umpiring, in the good old culture of baseball)! If some observation happens that flies in the face (or puts a fly in the ointment!) of a beautiful idea you really loved -- well, try other experiments and do other analysis to check that data... but then if it really holds up, HEY, we've learned something NEW! In life in general (not just science), we all have to cultivate the grace to be able to jettison our wonderful ideas (when evidence indicates it to be appropriate), with a Zen-like non-attachment! A key idea from logic that is central to the scientific method is the "contra-positive" -- which says that the statement "A implies B" is equivalent to "NOT B implies NOT A". This is basically the same as what I just talked about, above -- but here's a fun example, in the spirit of the scientific enterprise. Let's say we're at some ancient flat site where there's an archaeological dig going on, and a few short towers of diamonds have been found not far underground -- as well as one bigger obelisk of solid gold, at the same

6 level. So far, the distances of the diamond towers from the gold obelisk are all the same -- which prompts some observers to speculate that maybe what we're uncovering is a structure like Stonehenge or an American Indian "medicine-wheel", where in this case the diamond towers are arranged in a single circle around the golden obelisk. That's a reasonable hypothesis, given the equal distances thus far found beween the diamond towers and the gold obelisk.... Ah, look now, over here! They've just found another diamond tower, and it also is that same distance away from the gold obelisk! Well, that surely tends to confirm our hypothesis -- but it by no means proves it! If just one diamond tower is found at some different distance from the one gold obelisk -- or, if just one more gold obelisk is found in some different spot -- that would belie our whole theory. We'd have to come up with something else.... So, let's phrase this in terms of the contra-positive: "A" is the theory that we're onto a single circle of diamond towers surrounding a golden obelisk at the center. "B" is a logical (or mathematical) implication of this theory: the prediction that any further finds of diamond towers had better be at the same distance as all the others, from the golden obelisk. So, A implies B. If we find even just one diamond tower that is not at that same distance away from the golden obelisk -- i.e., if we find NOT B -- then A can't be right after all: NOT A! We don't have a circle of diamond towers around that golden obelisk -- attractive as that prospect was starting to seem!... So,... "If A, then B" means exactly the same as "If NOT B, then NOT A". That is, if B doesn't hold true, then A can't either -- because if A did hold, then B would have to, also! (If A, then B, remember?) Keep on thinking about this from time to time, until it comes naturally (if it doesn't already). In the above, another way of characterizing that relationship between A and B would be to say that A is a SUFFICIENT condition for B, but B is a NECESSARY condition for A. For B to be the case, it's sufficient to have A to be true, because A implies B. But for A, it's necessary to have B -- because NOT B implies NOT A.

7 If you can really grok this basic but all-important picture, you'll have the key to not only the whole scientific enterprise (not to mention our six-letter word game!), but also for cutting through the baloney in countless political and other arguments! ( ~ global warming... ) ============== And here's a response from an old high-school friend of mine back east -- and my response to his question Robert W Pickett wrote: > Joe: > > As for the gold/diamond analogy, why does it have to be if NOT B, then NOT A? Isn't "If NOT A, then NOT B" just as appropriate and correct? > > And, yes, it's easy to understand from your description. > > Keep it up! > Bob Pickett Hi Bob -- Thanks for the thought and reply! "(A) implies (B)" is actually not equivalent to "(NOT A) implies (NOT B)". It's only equivalent to "(NOT B) implies (NOT A)". If A implies B, and (NOT A) implies (NOT B), then A and B are equivalent -- i.e., we have "B if and only if A." In this gold/diamond example, you could have NOT A (i.e., not a circle of diamond towers around one gold obelisk), but still have B (equal distances of all diamond towers from the gold obelisk) -- if, say, the diamond towers are arranged as a cross -- corners of a square. I.e., there can be reasons other than A, for B to still be

8 true. All that "A implies B" says is that A is one reason for B to be true. (A is a sufficient condition for B.) That said, I realize that maybe I haven't set up the best example here, because (as you may well have already protested by this point) the corners of a square ARE certainly a SUBSET of points on a circle -- just as any finite number of diamond towers could also be only a subset!... So here's another example to demonstrate the logic I'm trying to elucidate -- but it's just not nearly as colorful or engaging, even though it is pretty ironclad: A = "I'm thinking of the number 7." B = "I'm thinking of a number less than 10." Here, clearly A implies B -- but it's not true that NOT-A implies NOT-B. However, it is still true that NOT-B implies NOT-A.!... Hmmm... So now, I'm wondering if I should try some better example. Thanks for your thoughts!... Maybe I could have my condition A instead be, "The pattern we're discovering here was originally intended to depict a circle." That would work -- and it's still interesting, because other very realistic possibilities would be that those ancient people had in mind a pentagon, or an octagon! (Each of those would indeed satisfy B, but not A.) And it's kind of fun, because there's that sense of trying to decode some ancient message or image. Whaddya think? -- Joe ===============================