{"id":11623,"date":"2012-08-17T11:54:22","date_gmt":"2012-08-17T15:54:22","guid":{"rendered":"http:\/\/johnesimpson.com\/blog\/?p=11623"},"modified":"2012-08-17T11:54:22","modified_gmt":"2012-08-17T15:54:22","slug":"miracles-of-confusion","status":"publish","type":"post","link":"https:\/\/johnesimpson.com\/blog\/2012\/08\/miracles-of-confusion\/","title":{"rendered":"Miracles of Confusion"},"content":{"rendered":"

\"\"<\/a><\/p>\n

[Image: a grainy photograph of a couple of volcanoes someplace. (Maybe another<\/em>
\n planet.) Or are they? See the note at the foot of this post for more information.]<\/em><\/p>\n

From\u00a0whiskey river<\/em><\/a>:<\/p>\n

Dharma<\/strong><\/p>\n

The way the dog trots out the front door
\nevery morning
\nwithout a hat or an umbrella,
\nwithout any money
\nor the keys to her doghouse
\nnever fails to fill the saucer of my heart
\nwith milky admiration.<\/p>\n

Who provides a finer example
\nof a life without encumbrance —
\nThoreau in his curtainless hut
\nwith a single plate, a single spoon?
\nGandhi with his staff and his holy diapers?<\/p>\n

Off she goes into the material world
\nwith nothing but her brown coat
\nand her modest blue collar,
\nfollowing only her wet nose,
\nthe twin portals of her steady breathing,
\nfollowed only by the plume of her tail.<\/p>\n

If only she did not shove the cat aside
\nevery morning
\nand eat all his food
\nwhat a model of self-containment she
\nwould be,
\nwhat a paragon of earthly detachment.
\nIf only she were not so eager
\nfor a rub behind the ears,
\nso acrobatic in her welcomes,
\nif only I were not her god.<\/p><\/blockquote>\n

(Billy Collins\u00a0[source<\/em><\/a>])<\/p>\n

…and<\/a>:<\/p>\n

Tour<\/strong><\/p>\n

Near a shrine in Japan he’d swept the path
\nand then placed camellia blossoms there.<\/p>\n

Or — we had no way of knowing — he’d swept the path
\nbetween fallen camellias.<\/p><\/blockquote>\n

(Carol Snow [source<\/em><\/a>])<\/p>\n

<\/p>\n

Not from whiskey river<\/em>:<\/p>\n

People have reality-dampers.<\/p>\n

It is a popular fact that nine-tenths of the brain is not used and, like most popular facts, it is wrong. Not even the most stupid Creator would go to the trouble of making the human head carry around several pounds of unnecessary gray goo if its only real purpose was, for example, to serve as a delicacy for certain remote tribesmen in unexplored valleys. It is<\/em> used. And one of its functions is to make the miraculous seem ordinary and turn the unusual into the usual.<\/p>\n

Because if this was not<\/em> the case, then human beings, faced with the daily wondrousness of everything, would go around wearing big stupid grins, similar to those worn by certain remote tribesmen who occasionally get raided by the authorities and have the contents of their plastic greenhouses very seriously inspected. They’d say “Wow!” a lot. And no one would do much work.<\/p>\n

Gods don’t like people not doing much work. People who aren’t busy all the time might start to think<\/em>.<\/p>\n

Part of the brain exists to stop this happening. It is very efficient. It can make people experience boredom in the middle of marvels.<\/p><\/blockquote>\n

(Terry Pratchett\u00a0[source<\/em><\/a>])<\/p>\n

…and:<\/p>\n

The usual techniques for proving things are often inadequate because they are merely concerned with truth. For more practical objectives, there are other powerful — but generally unacknowledged — methods. Here is an (undoubtedly incomplete) list of them:<\/p>\n

Proof of Blatant Assertion:<\/strong>
\nUse words and phrases like “clearly…,””obviously…,””it is easily shown that…,” and “as any fool can plainly see…”<\/p>\n

Proof by Seduction:<\/strong>
\n“If you will just agree to believe this, you might get a better final grade.”<\/p>\n

Proof by Intimidation:<\/strong>
\n“You better believe this if you want to pass the course.”<\/p>\n

Proof by Interruption:<\/strong>
\nKeep interrupting until your opponent gives up.<\/p>\n

Proof by Misconception:<\/strong>
\nAn example of this is the Freshman’s Conception of the Limit Process: “2 equals 3 for large values of 2.” Once introduced, any conclusion is reachable.<\/p>\n

Proof by Obfuscation:<\/strong>
\nA long list of lemma<\/span>s is helpful in this case — the more, the better.<\/p>\n

Proof by Confusion:<\/strong>
\nThis is a more refined form of proof by obfuscation. The long list of lemmas should be arranged into circular patterns of reasoning — and perhaps more baroque structures such as figure-eights and fleurs-de-lis.<\/p>\n

Proof by Exhaustion:<\/strong>
\nThis is a modification of an inductive proof. Instead of going to the general case after proving the first one, prove the second case, then the third, then the fourth, and so on — until a sufficiently large n<\/em> is achieved whereby the n<\/em>th case is being propounded to a soundly sleeping audience.<\/p><\/blockquote>\n

(Armen H. Zemanian, reportedly published in The Physics Teacher<\/em>, May 1994 [canonical source not available online<\/em>])<\/p>\n

…and:<\/p>\n

Why They Turned Back\/Why They Went On<\/strong><\/p>\n

Because a black bird flew across the road;
\nBecause the attendant at the pump turned surly;
\nBecause the uncertain weather
\nMade Mother nervous,
\nAnd, back home, the telephone kept ringing
\nIn an empty house;
\nBecause a white bird flew across the road.<\/p>\n

How far had they come?
\nHow far did they go?<\/p>\n

Seeing, along river after river,
\nBetween shores of brush and willow,
\nOnly the bend ahead and the bend behind
\nUnder a sky featureless and hard
\nAs a shallow bowl; through tautologies
\nOf a landscape unendingly repeated
\nMile after mile; down Main Street
\nAfter Main Street, replications
\nOf the same petty civic scenery;
\nHearing the ghosts of trains
\nCrossing between cornfields,
\nClattering over the points, moaning
\nAbove creosote and cinders,
\nAs if the imagination
\nCould produce nothing more
\nThan the same landscape, cornfields,
\nRivers, and Main Streets
\nPulling them, like a magnet, not toward
\nBut away from, not into the future,
\nBut away from the past;<\/p>\n

Until a white bird flew across the road
\nWith its mysterious message, that said to some,
\n“Turn back,” and to the rest, “Go on.”<\/p><\/blockquote>\n

(Constance Urdang [source<\/em><\/a>])<\/p>\n

___________________________________<\/p>\n

About the image:<\/strong> Unremarkable, isn’t it? It’s a little hard to picture just where on Earth these volcanoes (or whatever they are) might be, but otherwise it’s very straightforward. If not on Earth, obviously they’re volcano-like features\u00a0somewhere<\/em>.<\/p>\n

Unless, well, unless they’re not. Consider:<\/p>\n

\"\"<\/a><\/p>\n

From the page at the Stanford University site<\/a> where I found these images:<\/p>\n

The images… are the same except for being flipped (not rotated) up and down using a simple image processing program.<\/p>\n

If you rotate this book by 180 degrees, you will see that the mound in [the first figure] changes into a crater, and conversely the crater in [the second image] changes into a mound. When we interpret these shapes, we assume that the illuminant is elevated. This assumption about the position of the illuminant guides our inference about the shape of objects in the image. The distinction between mound and crater in these images is mediated mainly by the shading differences. Hence, rotating the images changes the shading relationship and we reinterpret the shape. Ramachandran (1988; see also Knill and Kersten, 1991) has demonstrated this phenomenon in a number of different ways. He argues further that the brain simplifies the interpretation of images by assuming the illumination consists of a single light source.<\/p><\/blockquote>\n

I found another demonstration of the principle here<\/a>, using the famous photograph of Buzz Aldrin’s footprint on the surface of the moon. The blogger there adds, though:<\/p>\n

No matter which version of the photo you are observing, if you contort yourself and try to look at it upside down, it won\u2019t switch — your brain simply won\u2019t permit it.<\/p><\/blockquote>\n

My brain won’t permit it, all right: it flat-out refuses to let me “contort myself” this way in the first place. :)<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

[Image: a grainy photograph of a couple of volcanoes someplace. (Maybe another planet.) Or are they? See the note at the foot of this post for more information.] From\u00a0whiskey river: Dharma The way the dog trots out the front door every morning without a hat or an umbrella, without any money or the keys to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","h5ap_radio_sources":[],"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":3,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[247,1393,95,250,5,36,251],"tags":[142,442,1141,2174,3144,3145,3146],"class_list":{"0":"post-11623","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-ruminations","7":"category-whiskey-river-runningaftermyhat","8":"category-science-medicine","9":"category-art","10":"category-06_writing","11":"category-reading","12":"category-poetry-writing_cat","13":"tag-terry-pratchett","14":"tag-dogs","15":"tag-billy-collins","16":"tag-optical-illusions","17":"tag-carol-snow","18":"tag-armen-h-zemanian","19":"tag-constance-urdang","20":"entry"},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6kZSG-31t","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/posts\/11623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/comments?post=11623"}],"version-history":[{"count":13,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/posts\/11623\/revisions"}],"predecessor-version":[{"id":11636,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/posts\/11623\/revisions\/11636"}],"wp:attachment":[{"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/media?parent=11623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/categories?post=11623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/johnesimpson.com\/blog\/wp-json\/wp\/v2\/tags?post=11623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}