Now you really are who they think you are

kw: book reviews, nonfiction, public relations, reputation

The Securities and Exchange Commission has an interesting provision to avoid market melt-downs caused by high-speed "robot trading"; when certain criteria are met, time delays are inserted between market orders and market fulfillment. There is no similar provision when a "reputation error" goes viral and someone's life is ruined in a matter of minutes. The old saw has it, "It takes a lifetime to build a good reputation, and five minutes to ruin it." Way outdated. A rumor, true or mistaken, can circle the Earth in a second or less, and there's no getting all the toothpaste back in the tube.

Disclaimer on the author's part: Michael Fertik founded Reputation.com, so some might consider his new book to be an advertisement. Regardless, The Reputation Economy: How to Optimize Your Digital Footprint in a World Where Your Reputation is Your Most Valuable Asset, written with his colleague David C. Thompson, is filled with useful information and advice.

Some folks are concerned about identity theft or identity fraud, and the banking and credit card industries are gradually learning how to forestall or recover from the most common kinds of such attacks. But not many of us are ready for the leap from "big data"—such as the records being kept of all phone calls, texts, IM messages and so forth—to "big analysis". Big Analysis has two parts. Firstly, computer programmers are getting more and more able to produce programs that extract meaningful correlations across huge masses of data. Secondly, the CPU's, the "brains" of computers, continue to get faster and multi-CPU clusters are being coupled with better and better sharing systems to break up large problems into smaller chunks for even more efficiency. This latter fact is the reason that weather forecasts have gone from the sort-of-iffy 3- or 4-day forecasts of the 1980s to remarkably competent 7- to 10-day forecasts today.

The time was, you could rely on "security by obscurity" to keep most of your activities below the radar, not only of law enforcement (if you had reason to fear them), but of businesses that could profit from intimate knowledge of your preferences and activities, such as insurance companies and potential employers.

Scenario: You apply for a job at Universal Widget Co. In the age of snail mail, your résumé would arrive the day after you mailed it, and if you were lucky, some HR manager would have only a dozen or so résumés to read, and would like yours well enough to phone you to come in for an interview. But today? Many companies don't accept paper résumés, but want either a PDF (machine-readable of course) or a file readable by MS Word or Word Perfect. And the HR department has received 200-1,000 résumés, so no human will have a first look. Keyword-checking software will weed out all that don't seem to meet minimum criteria, and those that pass this stage may be subject to further automated checking in the records of colleges you claim to have attended and former employers. At this point, 5 or 10 surviving résumés are probably read by a human, who may initiate further electronic searches, such as FaceBook, Twitter, and other social media sites. You get a positive score (P) for criteria met and other character traits that seem helpful, and a negative score (N) for anything they might not like, such as photos of yourself jamming it up in a bar scene, or perhaps skydiving or SCUBA caving. The N score is subtracted from the P score, and at most the top 3 candidates—if indeed anyone still has some P points left—get a call for an interview, in the order of their scores. To paraphrase one question the authors ask, do you have enough moxie, and luck, to satisfy both the machines that judge your résumé and the person who might eventually read it?

The above is a DAMM, a decision almost made by machine. Almost. Actually, for everyone but the 5-10 the HR person actually perused, it was a simple DMM; no "almost" about it.

The greatest lesson of the book for me is that absolutely everything we do that touches the systems of electronic watchdogs out there gets kept forever. Even if an error so blatant you could win a libel suit occurs, and you get some records deleted, somebody already has copies (hundreds of somebodies, most likely), you don't know who they are, and any fact from your past can crop up at any moment. Murphy's Law practically demands it will pop up at the worst possible moment.

Consider:

• Every search engine, not just Google or Yahoo!, keeps every search made along with a record of the IP address it came from. (I foretell a large increase in use of library computers) These get sold to anyone with sufficient cash, at a few cents per million. Google alone processes 3-4 billion searches daily.
• Your cell phone is constantly "pinging" so it knows where the nearest cell tower is. About every 15 minutes, more or less, and it depends on which generation (2G, 3G, 4G) your phone is. In urban areas, your travels can be tracked with an accuracy of a few blocks. In rural areas, the tower spacing is a couple of miles. Of course, when you are on a call, or sending and receiving texts, a new fix is made on your location several times per second. And that is with the phone's GPS turned off!
• Everything we write, every picture or video we post—or post a link to—is kept. Big Analysis can figure out not only your own proclivities, but those of your FB friends or Twitter followers, and it is human nature to resemble our friends. So if you, for example, work for a prison ministry, use a company FB account to "friend" the inmates! And make sure they know you by a handle that is hard to guess from your name. Many young adults in our son's generation use a pseudonym on FB, also. 
• Cameras are everywhere. In London, probably at least one on every street corner. Other cities are catching up fast. A friend with a tiny hole-in-the-wall store has 9 cameras in it. It takes very sophisticated methods to confuse a person-recognition camera. Not just how your face looks, but the way you walk or turn your head.

That's just a few items. Do you have "loyalty cards" from stores you use a lot? I just checked my wallet. I carry 5: 2 from groceries, and one each from Sears, a sporting goods store, and a pharmacy. I have several more in a dresser drawer. But that puts me behind the times. Many folks carry 15, 20 or more. All those stores know something about what you like. Whoever has bought all their data (I am sure someone has done so) may know you better than you know yourself! And there are other bits at PayPal, eBay, Amazon, and so it goes.

The biggest piece of advice? Take charge of your reputation. Brag on yourself. Make creative use of Endorsements in LinkedIn and encourage your LI friends to Endorse you; it is no longer considered bad form to point out the strengths you'd most prefer to have Endorsed. If you just have to rant about something, or, most importantly, someone (such as a boss!), do so using an electronic venue that isn't linked to "the rest of you". Future employers are wary of people with anger management issues.

To live in the modern world, we must assume privacy is a thing of the past. So, like someone who might be a bit overweight but wants to look thinner, wear looser clothes, metaphorically speaking, and hang out with people just a little "thinner" than you are. That last seems counterintuitive, but remember this is about reputation. Sure, you'll look thinner if you hang out with fatter people, but someone looking on will expect you to change to be more like them. Substitute your "negative trait of choice" for "overweight" and "fat" above, and its counter-virtue for "thin".

We are still learning to live with TV poking into everything. Now everything can poke its nose into our affairs. We just need a little reputation jiu-jitsu, and this book has at least a few pointers on how to learn some. If I could get just one law passed, a good one might be to mandate a 5-minute delay between hitting "Send" and the delivery of a Twitter post or similar item. Maybe a bigger and bigger delay, the more people it is sent to. Think about it…

Rescue Cat

kw: book reviews, nonfiction, cats, homelessness, street life

There are dog people and cat people (and small numbers of a few other kinds). I am a cat people. Raised with them. Raised many. Not quite raised by a cat, but then, I didn't have a cat like Bob. I suspect he could have managed it.

Bob is the star of two books by James Bowen. I haven't seen the first one yet (A Street Cat Named Bob), but I'll get to it anon. I just finished reading The World According to Bob. Quite an amazing book. I wondered how someone like Mr. Bowen could write a book, but since a third of the second volume is about how the first volume came to be, I didn't have to wonder long.

James Bowen was a troubled young man who fell into drugs as a teen and was a heroin addict for about a decade. I presume his ascent from the depths of addiction is mainly covered in the first book. This one begins with him being on the mend for a further decade, and being weaned from Methadone treatment, and finally the follow-on remedy, Subutex. But he remains desperately poor, though he is eking out a bit of a life in a flat, the kind that you have to "top up" the heat and electricity meter almost daily. He has spent some years selling a street publication, then has to return to busking (he's a guitarist and singer), which he'd done so many years earlier.

Bob, a ginger tabby, has been his constant companion since 2007. People are suckers for a nice animal, so having Bob on hand helped James sell more of the magazines, more than offsetting the vet bills. But Bob has not been a passive cat, for viewing only. He plays to whatever audience comes by, and even does a "high 5" at times with James or someone else. It tends to stop people long enough to induce them to buy a magazine, or later on, to toss a quid or two into the hat.

One of the aims James has in both books is a frank portrayal of street life. People's habitual disgust at someone disheveled and dirty, and probably smelly, pushes them farther and farther into the margins of society. And many folk wish they could be pushed right out of all possible view.

Both James and Bob had to navigate a significant transition once the first book was published. Anywhere you may be, some folks are going to envy any break you might get. On the street, people tend to be less reserved about expressing an opinion, particularly when it is contrary. Fortunately, the publishing company folks have done more than just assign and interviewer to gather the stories and knock them into a narrative in James's voice, and market the book. He had help of many kinds along the way.

When a cat adopts you, perhaps in many cases it is just trying to secure a steady meal plan. But once in a while a cat is more like Bob, and becomes a partner in your life, even defending you and yours. One would-be mugger has a few rather large scars that prove that. The chapter titled "Doctor Bob" further shows this; our pets are keen to our welfare, and Bob sometimes seemed to know what had to be done about it. We don't often think that the life of a homeless or poor person is fraught with more illness and pain than is usual among "middle class" people. James benefited an amazing amount from Bob's presence and ministrations.

I am glad that one man at least has been helped to rise from the street, and is likewise helping others. He owes a lot of that to the cat named Bob. See where they are not at their blog.

Scrabble® training level zero

kw: book reviews, nonfiction, wordplay

I knew there were more 2-letter words than most folks think of, but I didn't know there are 101. According to Stephin Merritt's introduction to 101 Two-Letter Words, the official list of "acceptable" words you can use playing Scrabble® is 101.

Anyway, Merritt is a songwriter, and a fast hand with a rhyme, so when he found himself writing cute quatrains for various 2-letter words, he decided to do them all. With the help of Roz Chast, whose cartoons you might have seen in New Yorker and elsewhere, 202 pages were occupied with the rhymes such as this one for HO:

"Ho, ho, ho," says old Saint Nick,
But saint for what, exactly?
Mayhap for hopping round the world
and getting back intactly.

And here is Santa upon his return. I reckon you can see why I call the work of Ms Chast "charmingly ugly".

And I applaud them both for picking this meaning for HO in preference for another of more recent vintage.

It is interesting, of 676 possible 2-letter combinations, nearly 15% are considered words. I reckon that is the highest percentage going. But even a lower percentage for 3-letter words would still pile up to a lot, as there are 17,576 to start with, and nearly 1,300 (7.4%) that the Scrabble® folks count. That would make for a much bigger book.

The making of a man of God

kw: book reviews, nonfiction, christian faith, missionaries, learning the hard way

Those who heed God's call learn by experience that we are called to death and resurrection, not only in the future for our body, but in this life for our soul and spirit. One Christian writer wrote, to paraphrase a little, "At the Gate of heaven stands the Cross. Only what can pass through the Cross and arise is permitted to pass through the Gate and enter in."

The experiences of four men in the Bible illustrate this.

• Firstly, Moses is the prototypical Man of God of the Old Testament. He was educated and prepared for 40 years according to the Egyptian way, though he had secret contact with his Hebrew family. Then, in Stephen's words "he decided to visit his own people, the Israelites" (Acts 7:23). Thinking to help them, he ended up killing an Egyptian and was soon an exile. We recognize the next 40 years as a time of God's preparation, but all the while he thought he would always be a shepherd in Midian. Then God called him openly, and so began the third 40 years in which he served God and God's people.
• Secondly, David, the one God chose to be king over Israel (1 Samuel 16), was at first modest and retiring, but once he tangled with the ambitions of king Saul, he was forced to flee to the surrounding lands, where he was hardened into the man of war needed to defend the kingdom after he was crowned. It seems he lived for some time as the leader of a gang of bandits. As a well-versed Jewish women told me once, "David was a scoundrel!" Indeed he was. But he was God's scoundrel, one who was always willing to repent once shown his fault (see Psalm 51).
• In the New Testament, we will skip over the obvious choice of Jesus for the moment, and look at Saul of Tarsus. As a zealous young man he sought to serve God by imprisoning Christians and even voting in favor of their killing. Once God called him as he neared Damascus, his preaching at first caused lots of trouble. He had to be smuggled out of Damascus to save his life, and later had to be smuggled out of Jerusalem. We don't know how long he was in Tarsus, where he'd been taken. He wrote that he spent some time in Arabia, returned to Damascus, then spent 15 days with Peter in Jerusalem. Only after this, about three years later, did the Holy Spirit designate Barnabas and Saul to go out preaching as apostles.
• Now we come to the case of Jesus, the prototype of a Man of God for New Testament believers. What happened right after his baptism? He spent not 40 years, but just 40 days in the wilderness, where he confronted Satan and overcame his temptations. The difference between Jesus and Moses? The indwelling Holy Spirit in Jesus, and his own divine nature, so that his human nature could be fully and quickly conformed to God's will. As we find it written to the Hebrews (vv 5:7-9), "During the days of Jesus’ life on earth, he offered up prayers and petitions with fervent cries and tears to the one who could save him from death, and he was heard because of his reverent submission. Son though he was, he learned obedience from what he suffered and, once made perfect, he became the source of eternal salvation for all who obey him."

Any who would serve God will spend time in a wilderness, one of God's choosing. Jesus "learned obedience", not just in the wilderness overcoming the Devil, but continually over time, so that at Gethsemane, just before he was arrested, he had already passed through death and resurrection in his heart and was made ready for what was to come next.

Though none living today can compare with Moses, David or Saul/Paul, let alone Jesus, yet even a minor servant of God such as myself cannot serve effectively until the elements of the natural life die with Jesus and we are then raised in Jesus into newness of life. In my own case, there came a time that I said, more than once over a period of months, "All my dreams have died." Eventually, I heard the tiny, quiet voice ("gentle whisper" in NIV) of the Spirit, "What about My dream?" A church I—with others—had raised up a few years before, that crashed and burned, became a "learning experience". Two churches raised up in subsequent years remain healthy.

Whatever is our concept of serving Jesus, it is OUR concept, and matches HIS concept very loosely, if at all. It is His business to correct us, and we are unlikely to enjoy the experience. This is a lesson young Jonathan Hollingsworth learned, as we all do, the hard way, as recorded in the book Runaway Radical: A Young Man's Reckless Journey to Save the World, co-written with his mother Amy Hollingsworth. In the case of young brother Jonathan, the lesson came harder than most, for God was dealing with a most deadly enemy within him, his Legalism. This he tells us clearly.

Jonathan had a few experiences that cemented his faith from an early age. By the time he finished high school he was quite enamored of a "radical obedience" model of putting faith into action. He decided to attend no more than two years of college before going to Africa to serve God among the people there. With the help of his family and some fellow believers, and later the leaders of the church he attended, he set off for Cameroon, under the aegis of a missionary organization led by a man known in the book only as Peter.

By day three he was in love with the Cameroonians. By day six he knew he was in trouble with the organization, but a slippery slope once stepped on has a way of sending you careening out of control as you watch, helpless. Within a couple of months he was, effectively, a slave to an organization that was legalistic in the extreme. A key word here is "organization"; we will return to it. Once he was able to admit to himself, and then to his parents, that he was in real trouble, on a road to destruction, it took his parents and some of their friends another couple of months to extricate him from Africa.

If anyone ever had a right to say, "My dreams have died", it is Jonathan. Everything he hoped to accomplish in Cameroon became impossible. The organization had its own agenda for him, and would brook no interference from his puny will. No contact with "the wrong kind of Christians," that is, anyone not of that organization's network of "churches", was permitted; hardly any contact with his family was allowed to go "unsupervised"; at one point, he took badly sick, but because a meeting was scheduled, he was dragged there, and not allowed to hold his head in his hands, but his hands were forcibly raised in "the African way" of worship. Only after that was he taken to a doctor. No matter what was really going on with him, everything about him had to look good, even triumphant.

He suffered "house arrest" and near-total isolation for more than two months. It is God's grace that he had any sanity remaining by the time he returned home. Yet this was not enough. The "senior pastor" (who deserves not the title) coerced silence of him, wishing to continue working with Peter, the Devil in disguise. Jonathan was victimized yet again. But two years have passed since then, plus a good part of another in which the therapeutic effect of co-authoring the book did its work. He realized God never left him, and worked in the background, to open his eyes to the judgmental, legalistic youth he had been, and showed him what Grace really means: you don't need to earn God's approval by working yourself to death, because you begin with God's approval. You do not attain holiness by working for it, but are made holy by the Holy Spirit, and then gradually learn to live in spirit until that holiness shows when others observe you.

A word about organizations. A watchword I have learned is, "the church is organic, but is not organized." An organization cannot tolerate someone who makes it look bad; by visiting a couple who were "the wrong kind of Christian," but whose medical outreach was more effective than that of Peter's organization, Jonathan shamed it and suffered dearly for it. By learning the deep hypocrisy of that organization, he threatened to embarrass his family "church" (it is not!), and so he was, for a time, silenced.

Learn this well. A local church is not an organization. If you find an organization, you have not found a church. No organization can be a genuine church, no matter what they put on the sign board. One brother with whom I've worked fruitfully speaks of "the kitchen church-life", meaning a hot, messy place, just the antithesis of organized and political bodies by whatever emptily holy name they might use. But it is a place of feeding. Kitchens are for preparing food.

I reckon Jonathan is 23 or 24 years old now. That is about the age at which I began to learn how to serve God, or so I thought. I was about 30 when my wife and I went out to join a few to establish a church, and 38 when I began to say, "All my dreams have died." Now 29 more years have passed, and I am still learning obedience, but I have learned to leave the dreaming to God! I think I am learning the lesson that Moses learned at the outset (but also over time): the Burning Bush.

Jonathan was a burning young brother, but what fuel was being burned? His own reserves. He burned out rather quickly, for which we thank God; how sorry a state would he be in if he were still struggling to heap materials onto his "strange fire" on God's behalf? Moses saw a thorn bush that was full of fire, but not consumed. God was saying to him, "You (and Israel) are just thorns, full of the curse upon Adam. Do not presume to help Me. I will use you to do My work, but I Myself will be the fuel for the fire." The words God spoke to him are even more telling: "Do not come any closer," God said. "Take off your sandals, for the place where you are standing is holy ground." (Exodus 3:5) God was saying, "Don't insulate yourself from My holiness. Get in contact with this holy ground and become holy."

And so God calls His servants today. Our own dreams must die, because they are not God's dream. We come to him an earthen vessel, but already full of "stuff" that God must remove so he can fill us with Himself. I will close with verses from two favorite hymns that express, to me, an excellent spirituality:

How much can we do for our Savior?
  How much for our dear fellow man?
The way to do more than we’re able
Is Jesus within to enable;
  Thus we can do more than we can.
—(v.1 of No. 906 at hymnal.net, where you can also hear the tune and see 3 more verses)

———

I take Thy promise, Lord, in all its length,
And breadth and fulness, as my daily strength;
Into life’s future fearless I may gaze,
For, Savior, Thou art with me all the days.

And all the other days that make my life,
Marked by no special joy or grief or strife,
Days filled with quiet duties, trivial care,
Burdens too small for other hearts to share.
—(vv. 1 and 5 of 6, of No. 575; we call this "The Days Song")

A challenging spiritual test

kw: book reviews, spiritual reading, faith healing, divine healing, sermons, exhortation

A friend loaned me a book to read, one that has become a test of certain beliefs I hold. It is Christ the Healer by F. F. Bosworth. First published in 1924, the book originally contained five chapters. During his lifetime (he died early in 1958, aged 81) he expanded later editions of the book, and his heirs posthumously expanded it further. I read the paperback edition of 1973.

I have been for more than forty years under a ministry that teaches thus:

• The Exodus plus Wilderness period of Israel's history was characterized by miracles including numerous cases of miraculous healing.
• Certain later prophets, particularly Elijah and Elisha, performed miracles, but those were purposeful and selective.
• There were a few, scarce miracles during the period between the testaments, particularly the miracle of the oil during the Maccabean restoration of the temple in Jerusalem. This event is commemorated with Hanukkah.
• Jesus performed miracles throughout his ministry (Apocryphal stories of miracles he performed as a child are fairy tales at best). He healed all who came to him for healing and raised at least three dead persons, including Lazarus.
• The apostles performed miracles, but more selectively as time went on. Paul in particular had a gift of healing which was with him throughout his ministry.
• Not all divine healing is miraculous. Some of the healings Jesus performed were instant, and thus miraculous. Others occurred over a period of time. God strengthened the healing abilities of the natural body.
• In Paul's later writings we find that he did not always heal the sick. Trophimus had to be left behind sick at one point, and Paul counseled Timothy to settle his sensitive stomach with wine.
• The author of the book of Hebrews, whom we believe was Paul, mentions the "powers of the age to come" (6:5), which we take to mean we have only a "taste" of miraculous works and divine healing in this age.
• God is purposeful, and is not to be treated as a magician that we can invoke for just anything.
• Thus, we conclude that divine healing does occur, but is not frequent, and instant, miraculous healing is quite rare indeed, in this period called the Church Age.

Bosworth would vociferously decry our conclusions. He is an absolutist. The only tiny concession he would make in our favor is found in a chapter titled "Why Some Fail to Receive Healing From Christ", in which he discusses 22 causes of such failure. Number 10 reads:

Sickness and affliction are permitted to remain on some as a halter, with which God leads them into the center of His will, and when this has been done, He removes the halter.

The other items are variations on three themes:

• The sick individual is at fault, either not believing rightly or not acting decisively upon the promise of healing.
• The evangelist or pastor is at fault for teaching improperly regarding divine healing (such as our teaching outlined above, if it is indeed improper).
• The "community", meaning a congregation or related group of congregations, is in a state of ignorance regarding God's will to heal all His children, thus hindering His work.

It is extremely clear from the sermons and testimonies in the book that Bosworth believed God's will is absolute, to bring to salvation every person who receives Him, and to totally heal every person who asks in faith for His healing. He bases both upon the Atonement of Jesus, making them equally inclusive promises, based on a number of Bible passages, most familiarly,

"Surely he took up our pain
    and bore our suffering,
yet we considered him punished by God,
    stricken by him, and afflicted.
But he was pierced for our transgressions,
    he was crushed for our iniquities;
the punishment that brought us peace was on him,
    and by his wounds we are healed." (Isaiah 53:4-5, NIV). 

Matthew quoted the Septuagint translation of the first half of verse 4, so that the NIV has it, "He took up our infirmities and bore our diseases." Of course, Bosworth used the Authorized Version (KJV), which has "sicknesses" in Matthew, but "sorrows" in Isaiah. That last phrase, "by his wounds we are healed", is an article of faith to faith healers.

There is a contention among expositors, whether "healed" at the end of verse 5 refers to bodily healing, or healing of the soul from iniquity. I believe it refers to both, but with the proviso that God heals, or performs other miraculous actions, according to purpose.

I find it quite refreshing that Bosworth writes, on page 77, "Even Laymen May Pray for the Sick". In his era, there was no thought of any kind of church polity among Protestants and Pentecostals other than the pastoral system. Since I consider that system invalid, and as Martin Luther taught, we enjoy "priesthood of all believers", of course every child of God may pray for healing the sick. Yet we also see in 1 Corinthians that God has set some in the church with special gifts including gifts of miracles and gifts of healing. Bosworth also distinguishes healing from miracles, at least in most cases.

Bosworth's theology is also founded upon the special names of God that he calls "Redemptive Names":

• Jehovah Shammah, the Lord who is Present
• Jehovah Shalom, the Lord our Peace
• Jehovah Ra-ah, the Lord the Shepherd
• Jehovah Jireh, the Lord will Provide
• Jehovah Nissi, the Lord our Banner (or Victor)
• Jehovah Tsidkenu, the Lord our Righteousness
• Jehovah Rapha, the Lord that Heals

He argues that the standing of the last name is equal to the other six, and is thus part of the promise of the Atonement of Christ. This is a strong argument, and if this were all the Bible, it would be unassailable. Yet what do we see of the attitude of Jesus of Nazareth towards miracle-seekers? John wrote,

"Now while he was in Jerusalem at the Passover Festival, many people saw the signs he was performing and believed in his name. But Jesus would not entrust himself to them, for he knew all people. He did not need any testimony about mankind, for he knew what was in each person." John 2:23-25

If we do not allow ourselves to be distracted by the new chapter that begins immediately after, we see how Jesus withdrew from those who were enamored of his signs (John always called the miracles and healings "signs"), but that he attended to the inquiry of Nicodemus, who saw beyond the signs to the One sent by God. And what are we to make of what Paul wrote to the Corinthians in chapter 13, the "love chapter"? He begins with four examples of spiritual gifts, tongues, prophecies, faith to move mountains (miracle working), and almsgiving, and shows that they are nothing without love (the famous word agape that speaks of love that has God as its source). Then in verses 8-10 he says all things other than love will cease, using three examples, prophecies, tongues, and knowledge. His word is inclusive, that the supernatural spiritual gifts were temporary. Indeed, in all his later epistles, he does not again mention the supernatural gifts, but instead writes of gifts that develop from growth in life, until the person is the gift to the church, under the titles Apostle, Evangelist, Prophet, Shepherd and Teacher, as seen in Ephesians chapter 4.

It is true, as Bosworth wrote, that healing is unlikely if we merely believe in God's ability to heal, or even if we merely hope in His healing. If we have, particularly with others, prayed a prayer of faith, and have an inner sense of God's affirmative answer, we must believe that we do have the healing already, even though symptoms may linger for a short time (days, not months). Bosworth uses the example of the fig tree that Jesus cursed. Nothing happened immediately, but the next morning the disciples saw that it had withered. It continued to appear the same at first. In the same way, after we sense that a prayer is answered, the symptoms may not disappear all at once. Testimonies in the last part of the book confirm such experiences. Some people experienced immediate and total healing. Others experienced a gradual release from symptoms.

Now, I have had a few experiences that make me wonder. Here are a few brief stories, three of them my own:

• The year after I received Christ, that is, 1967, a girl, a young sister, was healed at a youth camp I attended. She had a dental deformity, and her teeth stuck out forward at an angle. This was even somewhat evident when she kept her lips tightly shut, and it caused her great embarrassment. The second evening, a few others our age took her for a walk after dinner, and asked her to pray with them for definite and immediate healing by the Lord. As she told us the following day, "After we had been praying a while my mouth began to feel very warm. At first I could not move my hand. When I could move it, it also could feel the warmth, and then, that my teeth now fit properly in my mouth!" I saw her teeth both before and after, and this was indeed a remarkable case of instant, miraculous healing.
• Around 1970, a sister that we got to know a few years later contracted cancer. She was told she was terminal. Some sisters came to pray with her, and after a time they all felt that the Lord had given His promise to heal. Her symptoms abated over several days' time, and she is still alive and serving in a church in England.
• In 1973 I got pneumonia. Brothers I lived with prayed with me, but we felt nothing particular from the Lord. The evening came for the church's prayer meeting (I lived next door). I had just been lying there feeling sorry for myself for a few days, but I was very sorry to miss that meeting. After my housemates went to the meeting, I sat up in bed and began to read the book of Matthew. I read the whole Gospel in less than an hour's time. Then I got out of bed and went to the meeting, fully whole. I told them there I'd been healed by taking in the Word of God.
• One thing we disparaged quite a lot was a practice that became rather faddish before 1980 of "leg-lengthening". An elder with whom I was close had back pains, and was told by a Christian friend that these might be because he had legs of different lengths (I do, and we'll go there, momentarily). He was persuaded to go to a healing meeting. There, a healing evangelist had him stand and looked at him. Then, he had him sit, and the man just took the heel of his shorter leg and pulled gently while all prayed. This elder felt nothing, but when he stood again, his stance was different because his hips were now level. His back pain never returned.
• That even made me wonder about my experience a decade or more earlier. I had polio at age 18 months, and one leg was twisted. I was made to wear leg braces in an attempt to straighten it for two years, with only partial success. I learned to compensate so that few knew how hard it was for me to walk with a mostly normal appearance. At age 14 I attended a youth camp and our last evening a child evangelist preached to us. I was very touched. I recall walking alone in the woods trying to talk to God. It may be that I received Christ then, rather than 5 years later. But as I look back, I see that that I had a determination arise over the next few months to straighten my leg as much as possible. I had to think about every step. Over about a year, the bones were reshaped, and although the leg is still half an inch shorter than the other, and the foot on that side is nearly two inches shorter, the leg is straight and I walk normally and without pain. It may be that my actual experience of salvation occupied a 5-year span!
• Finally, in 2000, I had colon cancer. It was a rather late stage, but not metastasized beyond the perineum yet. A wizard of a surgeon replumbed me in a 5-hour operation. I also had an ordinary course of chemotherapy. I believe the biggest factor was that the whole church where we met (and still meet) prayed urgently for me. A few years later, the gastroenterologist who had made the initial diagnosis told me, "You are a trophy!" He had initially given me a 15% chance to live beyond one year, after the operation and chemo. Was divine healing involved? This particular case is unclear, but I give Glory to God nonetheless, for the love of fellow believers at the very, very least, and I take these past 14+ years as a sign that He is just not done with me yet!

Bosworth's book has led me to rethink everything I believe about divine healing. God may indeed strongly will for all His children to be kept in good health until He is ready to call them home. It is equally clear that, at least the "halter" mentioned by Bosworth is active in some cases. But there is a big gap between the level of healing advocated in the book, and the experience of most of God's children today. I am prayerfully considering these things, and it would be worth everyone's time to do so.

Math is a way of thinking

kw: book reviews, nonfiction, mathematics, mathematical thinking, mathematical games

In the realm of the English and Americans being "divided by a common language" (widely attributed to Shaw, but author not known), the abbreviation for "mathematics" is "maths" in England and "math" in the U.S. The term itself can be colloquially translated "learnèd techniques". Note the accent; thus, mathematics are techniques of those who are learnèd.

Matt Parker wants to make math—he writes "maths", being British—enjoyable. For most people, "Math is hard," to quote the talking Barbie doll. The funny thing is, we use math all the time. To make us more aware of our penchant for mathematical thinking, and to show us some ways to play in a mathematical way, he has written Things to Make and Do in the Fourth Dimension. He bills himself as a stand-up comic and mathematician. The book is subtitled "A Mathematical Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More".

Well, how can mathematics, which encompasses much more than mere number-work, be made enjoyable? Can it be FUN? In my case, Parker is preaching to the choir. I was the kind of geeky kid who did enormous long division problems for fun. The kind who angered a series of calculus instructors by correcting them during class (It took me decades to learn sufficient tact to brace a fellow with his errors in the privacy of his office).

To anyone who has survived the standard American curriculum and graduated from High School, we started with "four banger" arithmetic (add, subtract, multiply, divide), went on to just a bit of exponents and roots (in my day we learned to extract a square root with pencil and paper), then geometry and algebra (in either order), trigonometry, and, if you were a High School senior after about 1966, introductory calculus.

Once you'd been schooled in algebra and plane geometry, did anyone bother to tell you they are equivalent? that one can solve with straight edge and compass the same problems that are presented with X's and Y's and such? I thought not. Probably because they were taught by different teachers; the algebra teacher probably didn't know geometry all that well, and vice versa: nobody told them either!

OK, what's fun about math anyway? Do you remember π? That odd number a bit larger than 3 that has something to do with a circle? For everyday purposes we can use 3.14 or 3 1/7 or 22/7. If you get familiar with it, you can win bar bets and get the occasional free drink. Here's how. You make a bet with someone that the glass he or she is drinking from is bigger around than it is tall. Make sure to use the word "around" not "across". Most people will say, "No way!" If they take the bet, hand them a piece of string. Have the person wrap it around the glass, and mark the length, then hold it next to the glass. The mark will nearly always be above the rim. Why do I say, "nearly always"? Some drinking glasses are quite tall and thin, but not the kind you'll find beer in. So do this for preparation. Get some string and do the comparison using all the different kinds of drinking glasses you find around the house. It is likely that only a really skinny iced-tea glass will be taller than it is around. In a bar, just eyeball that the height is less than three times the width, and you'll be OK.

But fun with math is more than just bar bets. Parker's stand-up routine is based on math, and he writes of a number of card tricks that use mathematical methods. One well-used card trick bases its "clairvoyant" result on the fact that 27 is 3x3x3…and here you thought the deck a stage magician was using had all 52 cards in it! And there are the numbers for lovers (Parker calls them "amicable numbers"). The smallest "loving" pair is 220 and 284. All the factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110. Add those 11 numbers: the sum is 284. All the factors of 284 are 1, 2, 4, 71, and 142. Add those 4, and the sum is 220. You can sometimes buy a little "puzzle heart", in two pieces with 220 on one half and 284 on the other. There are other (mostly much larger) pairs of amicable numbers, if you want a more geeky puzzle heart made to order.

And on the subject of amicability, or better, there is that "optimal dating algorithm" of the subtitle. An algorithm is a recipe, for cooking up the solution to a problem. In this case, the problem is finding a compatible spouse. In an early chapter, Parker refers us to a few gents (very few early mathematicians were female) who showed that the "optimal testing proportion" of a string of dates is the square root of the total number of dates (with different people) you are prepared to embark upon. Thus, if you plan to allow up to two years for the search, and have time for one date weekly (Friday or Saturday, your choice), that is about 100 maximum dates. The square root of 100 is 10, so you use the first 10 dates to gather information, make your lists, compile the strong and weak points, and determine which person you dated is the most compatible potential spouse. Then, you continue dating new people until someone comes along who is better than the best of the first 10. Stop your search and propose marriage. Suppose you get to the end of the two years, and nobody beat "good old #7"? You can't go back, #7 probably already married someone else. And the chances are about 5% that the 2-year search will fail, statistically. Now what? You can shrink the chance of such failure this way. After the next group of 10, you drop your standard a little, say to better than the second-best of the first 10. There's more statistics one can do, but you'll probably get swept off your feet by someone unexpected long before you reach the 100th date anyway!

Number tomfoolery and some mapping stuff (like the 4-color problem) take up 9 chapters, and then we get into higher dimensions. The 4th dimension is just the beginning. Though it takes a while, we eventually read of a conjecture that requires the use of a space with nearly 200,000 dimensions! The fact that we are alive is sufficient proof to me that no 4D space exists, at least not one that can contact our 3D space. An entity who lives in a 4D space could reach inside us and stop our heart, or remove it for our inspection, as Regina and Rumpel do in episodes of "Once Upon a Time". Doing so would be as easy for them as it is for us to touch the middle of a circle drawn on paper. There is a bigger reason, though, that he mentions as an aside. Orbital mechanics won't work in 4D, not even a little bit. You can't get a planet to orbit a star in any dimension higher than 3. And this is why I deny "string theory", which requires either 10 or 11 dimensions for the math to work.

A lot of the ground the book covers is in the field of topology. Mathematical I may be, but topology is an area I have shunned. The author did more to give me at least a glimmer of topological understanding, than shelves of math books by others. But not more than a glimmer. It really depends how your mind works.

Clearly, in dimensional and topological math, Parker is a genius compared to me. I do find that he comes up short in other areas, however. For one, he mentions at one point his computer idling along at 2.7 GHz, and follows with a parenthesis and a footnote:

The parenthesis: "(2.7 gigahertz is a measurement of how many times its logic gates can be run every second).*"

The footnote: * Actually, this is how many times the processor performs commands in a second, each of which could involve more than one calculation. So this is a low estimate for comparison. A more dedicated me would research how many actual calculations it does per second, aka FLOPS.

The italics in the footnote are mine, and point out an error. The original parenthesis is correct. 2.7 GHz is the rate at which the processor's clock runs, and the clock controls the logic gates. Some hardware operations (what he loosely calls "commands") take one clock tick to run, others take more than one, usually two to four, but perhaps even more. So the basic hardware instruction rate is slower than 2.7 GHz, and 2.7 GHz (for the CPU in his computer) is the highest rate, and thus is a high estimate, not a low one as he states. Furthermore, FLOPS refers to FLoating-point Operations Per Second, where floating-point refers to the calculation of numerical quantities. A 2.7 GHz processor includes a special floating-point processor, these days called a math unit, and it tops out at several hundred MFLOPS (millions of FLOPS).

Back to areas in which our author shines. He presents a geometric proof that an infinite series can have a finite sum, using one based on Zeno's Paradox (though he doesn't say so). Zeno asked, if a runner (he called him Achilles) has two miles to run, first he runs a mile, then a half mile, then a quarter mile, and so forth: does he ever arrive? Of course we know that the second mile is run in about the same time as the first. But it is stated as 1 + 1/2 + 1/4 + 1/8 and so forth, a series that goes on forever. We know in our gut that the sum is 2. Here is the geometry:

It is easy to see that you can continue dividing by 2 as long as your patience holds out. The little blue square holds all the pieces I didn't have patience to draw.

This is the most ancient (known) example of a converging series. Most series diverge, and the one that is right on the edge is the sum of all reciprocals: 1 + 1/2 + 1/3 + 1/4 and so forth. The book has a very clear proof on page 289 that this sum grows without bound (I was careful not to use the word "infinity". That is for later).

For those who aren't afraid of exponents, the sum of reciprocal numbers to a power, where the exponent is close to one, has a finite sum as long as the exponent is greater than one, but grows without bound if it is one or less. Thus, 1/1ⁿ + 1/2ⁿ + 1/3ⁿ + 1/4ⁿ is finite even if n is 1.00000000001 (or add as many zeroes as you like, but keep that last 1 ).

OK, let's talk about infinity. A late chapter is called "To Infinity and Beyond" (nods to Buzz Lightyear). Do you recall the different kinds of numbers? For review:

• Natural numbers: 1, 2, 3, etc. Also called Counting Numbers.
• Integers: the Natural numbers plus zero and negatives of the Natural numbers.
• Rational numbers: Ratios of any two integers such as 1/2, 19/14, 32768/4195.
• Irrational numbers: All non-Integers that have unending, nonrepeating decimal parts. The most familiar examples are √2 and π, and most people remember at least 1.414 for the one and 3.1416 for the other.

As it happens, there are two kinds of Irrational numbers, but not everyone hears of them even in high school math classes. Firstly, Algebraic numbers are also called Computable numbers, because they are the solution to certain computations, primarily involving polynomials, such as square roots. Secondly, Transcendental numbers are a great deal trickier. Some of them such as π are found in trigonometric equations, and others such as e (2.71828...) in logarithmic and exponential expressions. But they are not "computable" the way square roots are.

With that under our belt, Algebraic irrational numbers are abundant and comparatively familiar. Transcendental numbers are difficult to deal with, and the ones that are known to be so are rather few. It is very difficult to prove that a certain quantity is a transcendental number. The odd thing is, it is not hard to prove that there are a lot of them lurking in the number line. In fact, the Transcendental numbers infinitely outnumber all the rest! A paradoxical phrase I learned in graduate school states:

Between any two transcendental numbers, there exists at least one algebraic number. Between any two algebraic numbers, there exists an infinite quantity of transcendental numbers.

Parker demonstrates this with an amusing analogy called the Hilbert Hotel, attributed to Georg Cantor (Hilbert and Cantor were math geniuses of roughly 120 years ago). Infinite busloads of several kinds of "guests", meaning several kinds of algebraic numbers, are accommodated in the hotel and can always be fit in. Then a bus with just the transcendental numbers between 0 and 1 shows up, and the hotel cannot hold them all. The proof is on page 413, and makes sense while I am reading it, but escapes me immediately thereafter!

This shows that there are at least two kinds of infinity, now called Aleph-0 (or -null) and Aleph-1. But it is not known if there is a different Aleph that is "larger" than Aleph-0 but "smaller" than Aleph-1.

I think Matt Parker genuinely believes that anyone could love and enjoy math, given the right approach. I'd agree only if we recognize that mathematical thinking of certain kinds may be universal among us humans, but that a great many branches of the math tree are forever beyond the reach of many people, no matter what kind of schooling or inducement is offered. Certain kinds of minds are required to do certain kinds of thinking. As I get older, I realize more and more the immense diversity of humankind. A political scientist, a journeyman carpenter, and a medical technician, all regularly think thoughts in realms that will forever be beyond my understanding. They can think thoughts I could never learn to think. That's OK. I think I have a few thoughts of my own that many other folks will never comprehend.

I'll go further. Look at your automobile. The days are long gone that a single person can design and build an entire auto, the way Carl Benz did in 1885. It takes about 8 different kinds of engineer to do so now. Even 40-50 years ago I could take out the motor and rebuild it (did so, 3 times). Now I couldn't get it out without a set of tools I can't afford.

But don't let my quibbles and quandaries discourage you from reading the book. Matt Parker writes delightfully, with a clarity that gets around the defenses we might have against allowing any more math to get into our overstuffed head. Reading this book is like looking through a microscope or telescope. It shows a new landscape, and you may not comprehend it all, but the view is worth it anyway.