Conference rusure::math

Well,

    I think the following may help. I have a program that requests for a string
then it requests for the minimum and maximum subsets of the string and it goes and 
produces all possible subsets.

ex.

 give the string: THIS IS A PHRASE

 give the minimum cardinality of the subsets, from =     4

 give the maximum cardinality of the subsets, to =     4
 
   13!            =   6227020800.00
   ( 13 -   4)!   =       362880.00
   4!             =           24.00
   13!/(  9!  4!) =             715

A list of all 715 possible combinations follows:


THIS THII THIS THIA THIF THIH THIR THIA THIS THIE THEI THIS THSA THAF THFH THHR
THRA THAS THSE THIS THIA THIF THIH THIR THIA THIS THIE THSA THSF THSH THSR THSA
THSS THSE THAF THAH THAR THAA THAS THAE THFH THFR THFA THFS THFE THHR THHA THHS
THHE THRA THRS THRE THAS THAE THSE TSEI TEIS TISA TSAF TAFH TFHR THRA TRAS TASE
TSIS TIIA TIIF TIIH TIIR TIIA TIIS TIIE TISA TSSF TSSH TSSR TSSA TSSS TSSE TSAF
TAAH TAAR TAAA TAAS TAAE TAFH TFFR TFFA TFFS TFFE TFHR THHA THHS THHE THRA TRRS
TRRE TRAS TAAE TASE TEIS TSIA TAIF TFIH THIR TRIA TAIS TSIE TESA TASF TFSH THSR
TRSA TASS TSSE TEAF TFAH THAR TRAA TAAS TSAE TEFH THFR TRFA TAFS TSFE TEHR TRHA
TAHS TSHE TERA TARS TSRE TEAS TSAE TESE TISA TISF TISH TISR TISA TISS TISE TIAF
TIAH TIAR TIAA TIAS TIAE TIFH TIFR TIFA TIFS TIFE TIHR TIHA TIHS TIHE TIRA TIRS
TIRE TIAS TIAE TISE TSAF TSAH TSAR TSAA TSAS TSAE TSFH TSFR TSFA TSFS TSFE TSHR
TSHA TSHS TSHE TSRA TSRS TSRE TSAS TSAE TSSE TAFH TAFR TAFA TAFS TAFE TAHR TAHA
TAHS TAHE TARA TARS TARE TAAS TAAE TASE TFHR TFHA TFHS TFHE TFRA TFRS TFRE TFAS
TFAE TFSE THRA THRS THRE THAS THAE THSE TRAS TRAE TRSE TASE ASEI SEIS EISA ISAF
SAFH AFHR FHRA HRAS RASE ASIS SIIA IIIF IIIH IIIR IIIA IIIS IIIE IISA ISSF SSSH
SSSR SSSA SSSS SSSE SSAF SAAH AAAR AAAA AAAS AAAE AAFH AFFR FFFA FFFS FFFE FFHR
FHHA HHHS HHHE HHRA HRRS RRRE RRAS RAAE AASE AEIS ESIA SAIF AFIH FHIR HRIA RAIS
ASIE SESA EASF AFSH FHSR HRSA RASS ASSE SEAF EFAH FHAR HRAA RAAS ASAE SEFH EHFR
HRFA RAFS ASFE SEHR ERHA RAHS ASHE SERA EARS ASRE SEAS ESAE SESE EISA IISF IISH
IISR IISA IISS IISE IIAF IIAH IIAR IIAA IIAS IIAE IIFH IIFR IIFA IIFS IIFE IIHR
IIHA IIHS IIHE IIRA IIRS IIRE IIAS IIAE IISE ISAF SSAH SSAR SSAA SSAS SSAE SSFH
SSFR SSFA SSFS SSFE SSHR SSHA SSHS SSHE SSRA SSRS SSRE SSAS SSAE SSSE SAFH AAFR
AAFA AAFS AAFE AAHR AAHA AAHS AAHE AARA AARS AARE AAAS AAAE AASE AFHR FFHA FFHS
FFHE FFRA FFRS FFRE FFAS FFAE FFSE FHRA HHRS HHRE HHAS HHAE HHSE HRAS RRAE RRSE
RASE SEIS ISIA IAIF IFIH IHIR IRIA IAIS ISIE IESA SASF SFSH SHSR SRSA SASS SSSE
SEAF AFAH AHAR ARAA AAAS ASAE AEFH FHFR FRFA FAFS FSFE FEHR HRHA HAHS HSHE HERA
RARS RSRE REAS ASAE AESE SISA SISF SISH SISR SISA SISS SISE SIAF AIAH AIAR AIAA
AIAS AIAE AIFH FIFR FIFA FIFS FIFE FIHR HIHA HIHS HIHE HIRA RIRS RIRE RIAS AIAE
AISE SSAF ASAH ASAR ASAA ASAS ASAE ASFH FSFR FSFA FSFS FSFE FSHR HSHA HSHS HSHE
HSRA RSRS RSRE RSAS ASAE ASSE SAFH FAFR FAFA FAFS FAFE FAHR HAHA HAHS HAHE HARA
RARS RARE RAAS AAAE AASE SFHR HFHA HFHS HFHE HFRA RFRS RFRE RFAS AFAE AFSE SHRA
RHRS RHRE RHAS AHAE AHSE SRAS ARAE ARSE SASE EISA AISF FISH HISR RISA AISS SISE
EIAF FIAH HIAR RIAA AIAS SIAE EIFH HIFR RIFA AIFS SIFE EIHR RIHA AIHS SIHE EIRA
AIRS SIRE EIAS SIAE EISE ESAF FSAH HSAR RSAA ASAS SSAE ESFH HSFR RSFA ASFS SSFE
ESHR RSHA ASHS SSHE ESRA ASRS SSRE ESAS SSAE ESSE EAFH HAFR RAFA AAFS SAFE EAHR
RAHA AAHS SAHE EARA AARS SARE EAAS SAAE EASE EFHR RFHA AFHS SFHE EFRA AFRS SFRE
EFAS SFAE EFSE EHRA AHRS SHRE EHAS SHAE EHSE ERAS SRAE ERSE EASE ISAF ISAH ISAR
ISAA ISAS ISAE ISFH ISFR ISFA ISFS ISFE ISHR ISHA ISHS ISHE ISRA ISRS ISRE ISAS
ISAE ISSE IAFH IAFR IAFA IAFS IAFE IAHR IAHA IAHS IAHE IARA IARS IARE IAAS IAAE
IASE IFHR IFHA IFHS IFHE IFRA IFRS IFRE IFAS IFAE IFSE IHRA IHRS IHRE IHAS IHAE
IHSE IRAS IRAE IRSE IASE SAFH SAFR SAFA SAFS SAFE SAHR SAHA SAHS SAHE SARA SARS
SARE SAAS SAAE SASE SFHR SFHA SFHS SFHE SFRA SFRS SFRE SFAS SFAE SFSE SHRA SHRS
SHRE SHAS SHAE SHSE SRAS SRAE SRSE SASE AFHR AFHA AFHS AFHE AFRA AFRS AFRE AFAS
AFAE AFSE AHRA AHRS AHRE AHAS AHAE AHSE ARAS ARAE ARSE AASE FHRA FHRS FHRE FHAS
FHAE FHSE FRAS FRAE FRSE FASE HRAS HRAE HRSE HASE RASE 

Enjoy,

Kostas G.

There are four pages following this page.  The first contains 613 words of
four or more letters each which are constructed from the phrase "THIS
IS A PHRASE".  The second contains 111 three letter words constructed from
those characters.  The third contains 32 two letter words, and the fourth
contains 15 one letter words.  Unfortunately, the method I used to find
the words forces everything to upper case, so some words may appear to be
duplicated when in fact they are pairs of words with the first in all lower
case, and the second with an initial capital.

I used SUBSTR.B36 on UPORT$:[AMARTIN] on TLE"":: to filter the original
list of words.  The search algorithm is separate from all the arcane
I/O considerations in the program.  I then used VMS EMACS's regular
expression pattern matching to sort the filtered list on the basis of the
size of words.  (I know that finite automata can't count, but I can.  I
used ^...$, ^..$ and ^.$ as the the patterns).  Not the absolutely most
automated method of accomplishing the desired end, but joining together a
few existing tools with a little interaction beats writing something from
scratch.

Sorry if the verbosity of this answer makes people cast about for reasons to
banish it to JOYOFLEX or something.  I don't intend to make a habit of
posting the results of such simple queries here.


AESTII		AHEAP		AHET		AHIR		AIAS
AIRA		AIRE		AIRISH		AIRSHIP		AIRT
AITESIS		APAR		APART		APER		APERT
APHESIS		APHETA		APHIS		APHRA		APHRITE
APHTHA		APIARIST	APII		APIS		APISH
APSE		APSIS		APTERA		ARATI		AREA
ARHAT		ARHATSHIP	ARIA		ARIES		ARISE
ARIST		ARISTA		ARISTEAS	ARITE		ARSE
ARSES		ARSIS		ARTHA		ARTIE		ASAPH
ASARH		ASARITE		ASEPSIS		ASHA		ASHER
ASHERAH		ASHES		ASHET		ASHIR		ASHPIT
ASITIA		ASPER		ASPIRATE	ASPIRE		ASPISH
ASSAI		ASSART		ASSATE		ASSE		ASSERT
ASSET		ASSETS		ASSI		ASSIS		ASSISE
ASSISH		ASSIST		ASSISTER	ASTA		ASTARE
ASTER		ASTERIA		ASTERIAS	ASTIR		ATAP
ATES		ATHAR		ATHERIS		ATHREPSIA	ATIP
ATIS		ATRESIA		ATRIA		ATRIP		EARTH
EAST		EATS		EPHA		EPHAH		EPISTASIS
EPITASIS	ERIA		ERST		ERTH		ESPRIT
ESTH		HAET		HAIR		HAIRE		HAPI
HARASS		HARE		HARISH		HARP		HARPA
HARPIST		HARSH		HART		HASH		HASHER
HASP		HASSAR		HASTA		HASTE		HASTER
HASTISH		HATE		HATER		HATH		HATHI
HATI		HATRESS		HEAP		HEAPS		HEAR
HEARST		HEART		HEARTH		HEARTS		HEAT
HEATH		HEII		HEIR		HEIRSHIP	HEIST
HEPAR		HERAT		HERS		HERSHIP		HEST
HIATE		HIPE		HIPER		HIPSTER		HIRE
HIRSE		HISH		HISPA		HISS		HISSER
HIST		HISTIE		HITHE		HITHER		IPHIS
IRATE		IRIS		IRISH		ISAIAH		ISARIA
ISATIS		ISIS		ISSEI		ISSITE		ITEA
ITER		ITHER		PAAR		PAHA		PAHARI
PAHI		PAIR		PAIS		PAISA		PARA
PARAH		PARASITE	PARATE		PARATHESIS	PARE
PARESIS		PARI		PARIAH		PARIES		PARIS
PARISH		PARISIS		PARITI		PARSE		PARSI
PART		PASH		PASHA		PASI		PASS
PASSE		PASSE		PASSER		PASSER		PASSIR
PAST		PASTA		PASTE		PASTER		PATA
PATAS		PATE		PATER		PATERA		PATERISSA
PATESI		PATH		PATRIA		PEAI		PEAR
PEART		PEAT		PERI		PERISH		PERIT
PERSIS		PERSIS		PERSIST		PERT		PERTISH
PESA		PESAH		PESS		PEST		PHAET
PHARE		PHARISAIST	PHASE		PHASES		PHASIS
PHIT		PHRASE		PHTHISIS	PIARIST		PIAST
PIASTER		PIASTRE		PIER		PIERIS		PIET
PIETAS		PIRATE		PIRATESS	PISE		PISH
PISS		PIST		PISTIA		PITA		PITARAH
PITH		PITIER		PRAISE		PRASE		PRASTHA
PRAT		PRATE		PRESS		PREST		PRIEST
PRIESTISH	PRISS		PRISTIS		PSHA		PTERIS
RAASH		RAIA		RAIA		RAIAE		RAIS
RAIS		RAISE		RAPE		RAPHE		RAPHIA
RAPHIS		RAPIST		RAPT		RASA		RASE
RASH		RASHTI		RASP		RASPISH		RASPITE
RASSE		RATA		RATE		RATH		RATHE
REAP		REASSIST	REHASH		REIS		REIT
REPASS		REPAST		REPS		RESH		RESHIP
RESIST		RESP		REST		RESTIS		RETIA
RETIP		RHAPIS		RHEA		RHEA		RIATA
RIPA		RIPE		RISE		RISHI		RISP
RISS		RIST		RITA		RITA		RITE
SAHH		SAIP		SAIPH		SAIR		SAITE
SAITHE		SAPA		SAPHIE		SARA		SARAH
SARE		SARI		SARIP		SARSA		SARSI
SART		SART		SARTISH		SASA		SASH
SATE		SATIRE		SATRAE		SATRAP		SATRAPESS
SEAH		SEAR		SEAT		SEIT		SEPIA
SEPS		SEPSIS		SEPT		SEPT		SEPTA
SEPTI		SERA		SERAI		SERAPH		SERAPIAS
SERAPIS		SERAPIST	SERI		SERT		SERTA
SESHAT		SESIA		SESS		SESTI		SETA
SETARIA		SETH		SETH		SHAH		SHAHI
SHAP		SHAPE		SHAPE		SHAPER		SHAPS
SHARE		SHARESHIP	SHARP		SHARPIE		SHARPISH
SHARPS		SHASTA		SHASTER		SHASTRA		SHASTRI
SHAT		SHEA		SHEAR		SHEARS		SHEAT
SHEATH		SHER		SHERIAT		SHERPA		SHESHA
SHETH		SHIAH		SHIER		SHIES		SHIEST
SHIH		SHIITE		SHIP		SHIRE		SHIRPIT
SHIRT		SHISH		SHITA		SHITHER		SHRAP
SHRIP		SHRITE		SIER		SIESTA		SIPE
SIPER		SIRE		SIRESHIP	SIRESS		SIRIH
SIRIS		SIRPEA		SIRSHIP		SISE		SISH
SISI		SISS		SIST		SISTER		SITA
SITAR		SITE		SITH		SITHE		SPAE
SPAER		SPAHI		SPAR		SPAR		SPARE
SPARSE		SPART		SPARTH		SPAT		SPATE
SPATHA		SPATHE		SPEAR		SPEISS		SPET
SPIER		SPIRAEA		SPIRATE		SPIRE		SPIREA
SPIRIT		SPIRT		SPISE		SPIT		SPITE
SPITISH		SPRAT		SPREATH		SPRET		SPRIEST
SPRIT		SPRITE		STAIA		STAIR		STAP
STAPES		STAR		STAR		STARE		STARSHIP
STASES		STASH		STASHIE		STASIS		STEP
STERI		STIPA		STIPE		STIPES		STIR
STIRP		STIRPS		STRA		STRAE		STRAP
STRASS		STRE		STREPSIS	STRESS		STRIA
STRIAE		STRIP		STRIPE		TAAR		TAHA
TAHR		TAIPI		TAISE		TAPA		TAPA
TAPAS		TAPE		TAPE		TAPER		TAPHRIA
TAPIA		TAPIR		TAPIS		TAPS		TARA
TARAI		TARAPH		TARASSIS	TARE		TAREA
TARI		TARIE		TARISH		TARP		TARPEIA
TARS		TARSE		TARSI		TARSIA		TARSIPES
TASH		TASHIE		TASS		TASS		TASSAH
TASSE		TASSER		TASSIE		TEAISH		TEAP
TEAR		TERA		TERAP		TERAS		TERP
TESS		TESSARA		THAI		THAIS		THAPES
THAPSIA		THAPSIA		THAR		THEA		THEAH
THEIR		THEIRS		THERIA		THESIS		THIASI
THIR		THIS		THRAEP		THRAP		THRASH
THREAP		THRESH		THRIP		THRIPS		TIAR
TIARA		TIER		TIPE		TIPHIA		TIRE
TISAR		TISHRI		TRAH		TRAIPSE		TRAP
TRAPA		TRAPES		TRAPS		TRASH		TRASHIP
TRASS		TRESPASS	TRESS		TRIAS		TRIP
TRIPE		TRIPHASE	TRIPHASIA	TRIPSIS		TSAR
TSARSHIP	TSHI		TSIA


AER	AES	AHA	AHT	AIR	AIT	APA	APE	APT
ARA	ARE	ART	ART	ASA	ASE	ASH	ASP	ASS
AST	ATA	ATE	ATI	EAR	EAT	ERA	ERS	ESS
ETA	HAH	HAP	HAS	HAT	HEI	HEP	HER	HET
HIA	HIE	HIP	HIS	HIT	IHI	IRA	IRE	IST
ITA	ITS	PAH	PAR	PAS	PAT	PAT	PEA	PER
PES	PHI	PIA	PIE	PIR	PIT	PSI	PST	RAH
RAP	RAS	RAT	REA	REH	REP	RET	RHE	RIA
RIE	RIP	RIT	SAA	SAH	SAI	SAP	SAR	SAT
SEA	SER	SET	SHA	SHE	SHI	SIA	SIE	SIP
SIR	SIR	SIS	SIS	SIT	SPA	SRI	SRI	TAA
TAE	TAI	TAI	TAP	TAR	TEA	THA	THE	TIE
TIP	TRA	TRI


AA	AE	AH	AH	AI	AR	AS	AS	AT
EA	EH	ER	ES	HA	HE	HI	IE	IS
IT	PA	PI	RA	RE	SA	SE	SH	SI
ST	TA	TE	TH	TI


A	E	E	H	H	I	I	P	P
R	R	S	S	T	T

If you want to know all the words you can find in a phrase such as
"THIS IS A PHRASE", it is silly on a computer to do it "like we do",
namely shuffle letters around, and see what combinations come up as
words.

In other words, it is silly to ask the computer to generate all
combinations of the original phrase and then see which are words.

THE BETTER SENSIBLE IDEA :

	Program the computer to scan its on-line dictionary *ONCE*,
	and for each word in it, see if the word can be made with
	"THIS IS A PHRASE", and print it out if so.  Such a loop
	runs quite quickly and tells you the whole answer.

/Eric

    A touch of brilliance, thank you. Now to find whose got the Shorter
    Oxford or the Websters on line. I'll go ask elsewhere
    thanks very much.
    Fraser_B
    

Re .3:

Was your comment directed at some note in particular?

Re .4:

You get a cookie (excuse me, "scone") if you find more words than the
list in .2.
				/AHM

Re .2, .5:  Are a few suffixed words missing (parties, hastier, harshest,
	    prissiest)?

Re .2, .3, .4:  What online dictionaries are available?

John

Re .6:

Dictionaries I have used might well be missing some "suffixed" words,
though none of them contain data on how to add such words to them (unlike a
dictionary I saw in college, which represented words compactly with some
kind of affix expression language).


I made my smaller dictionary by merging dumped lists from SPELL and
WORDS on the -20.  I hadn't tried hard to get ISPELL to dump its guts.
You should have the same access to such programs down in PDP-10 land
that I did at the time.
				/AHM

    
    
    Here is a really simple problem for most of you...
    
    I'm trying to help my girlfriend with her homework but it's been ages
    since I've done these things.  She gave me 15 word problems.  I solved
    14 of them but this last one has me stumped...
    
    Mr. Peobody leaves his laboratory to drive to his wayback machine.  He
    travels at 55mph.  He is 10 miles from his lab when Sherman realizes
    that Peobody forgot his royal fizzbin.  How fast will Sherman have to
    drive to catch up with Peobody in two hours?
    
    Also, I'll throw this one in just to make sure I'm doing them right
    (I'm pretty sure this was fine, but always worth doublechecking)
    
    Spock has 50 grams of substance that is 7.8% antimatter.  How much
    substance that is 0% antimatter will he have to add to make the total
    strength of antimatter 2%?
    
    I said 7.8(50)+0y=2(50+y)
    390=100+2y
    2y=290
    y=145 grams
    

    re .8 (antimatter)
    
    Did you consider the matter-anti-matter reaction which converts all of
    the anti-matter and a matching mass of matter into energy?
    
    Dick

    Ignoring the laws of physics, the "antimatter" answer looks correct.
    
    As far as Sherman goes, look at it this way:  Peabody is 10 miles away.
    In two hours Peabody will be 10+55*2=120 miles away.  How fast will
    Sherman have to drive to cover 120 miles in 2 hours?  You take it from
    there, but remember you are assuming acceleration from 0 to the answer
    in 0 time -- again violating the laws of physics.
    
    Who writes these books anyway?
    
      John

    
    Actually those werent the original problems, I changed them to protect
    the innocent (Dr. White and a cow) :').Dr. White still intends to
    violate the acceleration principle anyway :').
    
    Okay, so um, er... how can Mr. Peobody be written in an
    x = shermans speed type of format?  (thats how the U Lowell prof. wants
    it done I guess).  Let me see...
    
    
    scrap paper time...
    
    thanks for all the help!  :')
    
    

What is wrong with wording the answer to the "how fast"
question as "He must travel at an average speed of ..."?
No more problems with instantaneous acceleration.

Dan

RE: .10

I've never been quite happy with the acceleration issue.  Yes,
accelerating from 0 to a speed in 0 time is forbidden - not just
from 0 to 60 mph, but for any finite speed.  So, how the heck does
anything get moving at all?  This seems to be a cousin of Zeno's
paradox.  I'de take this up in the physics conference but I'de kinda
like to sort out the mathematics first before worrying about the real
world.  I'm sure the answer lies in the study of limits and
infinitesimals.

    Re: <.13>
    
I think you're confusing acceleration and velocity. Acceleration is the rate 
of change in velocity, with respect to time; while velocity is the rate of 
change in distance with respect to time (both are vector quantities). Thus, for 
a body travelling in a straight line with constant acceleration A (say 10 
metres/sec�) its velocity V is the antiderivative of its acceleration, and the 
total distance travelled, D is the antiderivative of the velocity, i.e.

	A = 10

	V = 10t

and	D = 5t�		(where t = time in seconds)

Any increase in velocity takes time. After 0 seconds (t=0) the object is still
stationery, since its velocity is then 10 x 0 = 0. At any given instant later,
(since its acceleration is constant) its velocity may be calculated as a linear
function of the time since it started moving, i.e. since its acceleration was 
0. At the end of one second, its velocity will be 10 metres/sec, and it will
have covered a distance of 5 metres; after 2 seconds its velocity is 20
metres/sec and it will also have travelled 20 metres - its average velocity at
this time will be 1 metre/sec. Since the body is accelerating constantly
(and was motionless when it began, i.e. when its acceleration was 0) its
average velocity will continue to increase, linearly as a function of time.

    There's nothing much mysterious about this. Velocity does not increase "in
    no time at all", other than the instant when inertia and friction etc. are
    overcome and the body is set in motion, when its acceleration and velocity
    become non-zero simultaneously. Does this help or have I only added to
    your confusion?

James.

    RE: .14
    
    I assure you I am not confusing acceleration and velocity.  I
    appreciate your clear explaination.  At only two points did you loose
    me.   Both times you wrote that the acceleration 0, not 10.  I suppose
    these might simply be typos.  In your example, at time 0, what is the
    acceleration?
    
    Your final paragraph gets to the heart of the matter.  You wrote, "...
    other than the instant when ...".  It is exactly that moment that I am
    most interested in.  My confusion remains constant on this point.

    RE: .14
    
    Okay, I think I understand.  Your last paragraph says the velocity and
    acceleration both become non-zero together.  So, then, does the
    acceleration jump from 0 to the constant 10 all at once?  Or is there
    some sort of hyper-acceleration?  The acceleration increases from 0 to
    10 a such and such a rate.  Once the acceleration reaches the value of
    10 it is held constant.

RE: .16

    Velocity (at least in classical mechanics) cannot be discontinuous.  If
    there is one time t0 at which something is moving at velocity v0 and
    another time t1 at which it is moving at velocity v1, then for any
    velocity vx between v0 and v1 there must be a time, tx between t0 and
    t1 at which the thing is moving at velocity vx.  In other words if
    you plot velocity against time there will be no perfectly vertical
    steps.

    Sometimes it is convenient to ignore that restriction.  If there is
    a very large but very short accleration it may simplify things to
    treat it as an instantaneous, discontinuous change in velocity.

    There is generally no such continuity restriction placed on
    acceleration, and so it is common, even usual to assume instanteous,
    discontinuous changes in acceleration.  If you think about it, most
    (all?) examples of changes of acceleration are actually continuous
    but very rapid.  But very, very, rapid changes of acceleration are
    so commonplace (for example, the deceleration of a hard ball slamming
    into a hard wall) that the utility of discontinuous descriptions is
    almost universal.

    There is a term used occasionally for the rate of change of
    acceleration, but it is so rarely used that I have forgotten what it
    is called (its a common word pulled into technical service).  I have
    seen as an academic exercise an attempt to define the names of still
    higher derivatives but I doubt that anyone has every really,
    unselfconsciously used them.

    The reason that the rate of change of velocity has a common name but
    the rate of change of acceleration does not is that acceleration has
    a fundamental role in mechanics -- in classical physics it figures
    in the definition of force, and in GR it has an even more fundamental
    role.  Higher order derivatives are simply descriptive of a particular
    situation, and do not appear in descriptions of fundamental laws.

    You could probably, if you wished, define a coherent completely
    continuous mechanics, where all problems are defined by changes in
    position which are continuous for all orders of derivative.  Your
    problem statements will then become unnecessarily complex at no
    particular gain.

    The answer to questions such as you've been asking would then be by
    reference to the next higher derivative of position over time for still
    smaller time periods, and so on for an infinite regress.  It would
    then, like Zeno's paradox, ulitimately be resolved by reference to a
    limit.  In virtually all cases, that limit would be in almost all cases
    the same as if you just stopped at acceleration.  Easier to simply say
    that both continuous and discontinuous changes in acceleration (and
    higher derivatives when occasionally needed) are "allowed".

				Topher

Maybe it will help to consider what happens to a golf ball when driven by a 
club. As you swing the club, it attains a certain velocity - say 50 MPH;
when it hits the ball, it decellerates a bit and loses perhaps 5% of its
velocity as you begin your follow-through. 

During the time that the club face is in contact with the ball, the ball
experiences a *huge* momentary acceleration that causes it to go from 0 to
about 90 MPH in a fraction of a second. The accelerative force is so great
that it distorts the shape of the ball, but as soon as the ball leaves the
club face the acceleration drops immediately back to zero, while the
velocity continues - air friction slows it down a bit. Acceleration affects
the ball only for a fraction of a second, but the velocity remains until
some other force - friction with air or ground, or hitting a tree or
something - causes decelleration again. If you calculate the acceleration
that the driver causes, you come up with thousands of feet/sec^2, but the
actual duration is on the order of milliseconds. 

The velocity figures above may seem strange, but the ball actually is 
moving faster than the club head because as the ball returns to its 
original shape while still in contact with the club head, it continues to 
accelerate. The club-ball contact also distorts the shape of the club 
shaft, and its restoration also speeds up the ball (graphite clubs are
better because they restore faster). 

    re .17
    
    >You could probably, if you wished, define a coherent completely
    >continuous mechanics, where all problems are defined by changes in
    >position which are continuous for all orders of derivative. 
    
    But of course, it wouldn't be realistic.  Continuity is just a
    convenient approximation for huge numbers of tiny jumps.
    
    fwiw,
    
    Dick
    

re .17,

>    There is a term used occasionally for the rate of change of
>    acceleration, but it is so rarely used that I have forgotten what it
>    is called (its a common word pulled into technical service).

                                         3    3
I have heard the unit of measurement of d s/dt  (or da/dt) referred
to as the "jerk," with 1 jerk = 1 meter per cubic second. :-)

Dan

RE: .20
                                         3    3
>I have heard the unit of measurement of d s/dt  (or da/dt) referred
>to as the "jerk," with 1 jerk = 1 meter per cubic second. :-)

    Now where did I leave my cubic second? -- I had it just a moment ago.

				    Topher :-)

    That like one of those clocks with four faces?  :-)

    The example in .8 can also be solved without reference to the actual
    speed of the original tourist - the incremental distance to be
    travelled in two hours (the chase time) is 10 miles (the tourist's
    lead), so the incremental speed is 5 mph.
    
    Speed of original tourist is 55 mph (isn't that some kind of magic
    number in the US for roads?), thus the chaser needs to travel at 60.
    
    Its easier in metric ;>)
    
    regards,
    Michael Watts.