# LISP - 2 exponent 0 = 1

161 views

### ilias

Sep 16, 2002, 10:52:27 PM9/16/02
to
must cleanup my mind.

3 apples

collect 3 more apples.

i have now 6 apples.

this is the concept of addition.

+

this i like.

2 exp 0 = 1

can anyone explain me this with apples?

### David Sletten

Sep 17, 2002, 12:23:38 AM9/17/02
to

ilias wrote:

Do you understand what (expt 2 2) means? 2 X 2 = 4.
Next, (expt 2 1) means (/ (expt 2 2) 2) => 2.
Following the pattern we reach (expt 2 0), which is (/ (expt 2 1) 2) => 1

This has nothing to do with Lisp but a lot to do with elementary school
mathematics.

### ilias

Sep 17, 2002, 12:47:46 AM9/17/02
to
David Sletten wrote:
>
>
> ilias wrote:
>
>> must cleanup my mind.
...

>> 2 exp 0 = 1
>>
>> can anyone explain me this with apples?

> Do you understand what (expt 2 2) means? 2 X 2 = 4.
> Next, (expt 2 1) means (/ (expt 2 2) 2) => 2.
> Following the pattern we reach (expt 2 0), which is (/ (expt 2 1) 2) => 1
>
> This has nothing to do with Lisp but a lot to do with elementary school
> mathematics.

you have confused me.

i've requested an explanation based on apples.

to cleanup my mind.

### Thien-Thi Nguyen

Sep 17, 2002, 1:44:23 AM9/17/02
to
ilias <at_...@pontos.net> writes:

> i've requested an explanation based on apples.

(expt apple 0) => seed (of power).

thi

### ilias

Sep 17, 2002, 2:08:55 AM9/17/02
to

3 - 1 = 2

3 apples.

i ate 1 apple.

the i have 2 apples.

2 exp 0 = 1

with apples.

explain.

### Thien-Thi Nguyen

Sep 17, 2002, 2:08:32 AM9/17/02
to
ilias <at_...@pontos.net> writes:

> explain.

done. understand.

thi

### ilias

Sep 17, 2002, 2:35:40 AM9/17/02
to

was not for me.

it was for you.

Sep 17, 2002, 3:00:01 AM9/17/02
to
* Thien-Thi Nguyen wrote:

> (expt apple 0) => seed (of power).

This is brilliant. Now I understand exponentiation. Thank you.[1]

Could you please also explain the Hawking-Penrose collapse theorem in
terms of oranges? You see I only understand oranges, although I read
somewhere that oranges are not the only fruit and so I am more-or-less
comfortable with apples too. I would prefer you to stick to oranges
though.

--tim

Footnotes:
[1] This should read:
Brilliant, this.
Exponentiation.
Understood.

### ilias

Sep 17, 2002, 3:12:53 AM9/17/02
to

bananas comes to my mind.

### Thomas Stegen

Sep 17, 2002, 3:58:20 AM9/17/02
to

You cannot multiply apples with apples. Here is
a more mathematical explanation. ^ is the expt
operator.

a^b / a^c = a^(b - c) Check this one for yourself
if you don't believe me

a^0 = a^(b - b) b = c since they must subtract
to zero

= a^b / a^b A number divided by itself is always 1

= 1

This is not a proof untill you prove the first equation.
That has been done time and time again though and is very
intuitive so that should be no problem.

HTH.

--
Thomas Stegen

### Espen Vestre

Sep 17, 2002, 4:23:41 AM9/17/02
to
ilias <at_...@pontos.net> writes:

> 2 exp 0 = 1
>
> can anyone explain me this with apples?

but of course. Suppose you have just planted a small apple tree which
gives you only apple this year, but it is of a fabolous breed: For
every year from now on, it will give you twice as many apples as the
preceding year. So, after n years it will give you (expt 2 n)
apples. And after 0 years it will of course give you 1 apple - (expt 2
n) = 1.

Now please explain why you think it's appropriate to ask questions of
elementary math on comp.lang.lisp.
--
(espen)

### ilias

Sep 17, 2002, 5:09:30 AM9/17/02
to
Thomas Stegen wrote:
> ilias wrote:
>
>> Thien-Thi Nguyen wrote:
>>
>>> ilias <at_...@pontos.net> writes:
>>>
>>>
>>>> explain.
>>>
>>>
>>>
>>>
>>> done. understand.
>>>
>>> thi
>>
>>
>>
>>
>> was not for me.
>>
>> it was for you.
>>
>
> You cannot multiply apples with apples. Here is

3 piles with 3 apples each.

3 times 3 apples.

9 apples.

3 apples * 3 apples =

i see.

you are right.

> a more mathematical explanation. ^ is the expt
> operator.
>
> a^b / a^c = a^(b - c) Check this one for yourself
> if you don't believe me

2^5 / 2^3 = 2^(5-3) = 2^2
2*2*2*2*2 / 2*2*2 = 2*2
8*2*2/8 = 2*2

ok this seems to fit.

>
> a^0 = a^(b - b) b = c since they must subtract
> to zero
>
> = a^b / a^b A number divided by itself is always 1
>
> = 1

understand.

>
> This is not a proof untill you prove the first equation.
> That has been done time and time again though and is very
> intuitive so that should be no problem.

a^b / a^c = a^(b - c)

how do i know that this equation is correct?

and even if:

isn't there a real-life-example for 2^0 = 1 ?

### ilias

Sep 17, 2002, 5:54:22 AM9/17/02
to
Espen Vestre wrote:
> ilias <at_...@pontos.net> writes:
>
>
>>2 exp 0 = 1
>>
>>can anyone explain me this with apples?
>
>
> but of course.

> Suppose you have just planted a small apple tree which
> gives you only apple this year, but it is of a fabolous breed:

> For every year from now on, it will give you twice as many apples as the
> preceding year.

> So, after n years it will give you (expt 2 n) apples.

> And after 0 years it will of course give you 1 apple - (expt 2 n) = 1.

the story does not fit.

>
> Now please explain why you think it's appropriate to ask questions of
> elementary math on comp.lang.lisp.

i was working on assimilating backquote-syntax.

while doing this, this question raised.

so this question is directly associated with Lisp.

but i don't know how.

sorry!

### Espen Vestre

Sep 17, 2002, 7:16:09 AM9/17/02
to
ilias <at_...@pontos.net> writes:

> i was working on assimilating backquote-syntax.
>
> while doing this, this question raised.
>
> so this question is directly associated with Lisp.
>
> but i don't know how.
>
> sorry!

I'm trying to assume that you're not here just to entertain or
annoy us, so here's a seriously meant piece of advice: If you're
going to ever learn programming (not to mention understand the
underpinnings of lisp!), you need a minimum of mathematics.

When you have that minimum knowledge, you'll know _several_
reasons why 1 is the right value when you extend the expt-function
from positive naturals (or reals) to naturals (or reals).
--
(espen)

### ilias

Sep 17, 2002, 7:32:55 AM9/17/02
to
Espen Vestre wrote:
> ilias <at_...@pontos.net> writes:
>
>>i was working on assimilating backquote-syntax.
>>
>>while doing this, this question raised.
>>
>>so this question is directly associated with Lisp.
>>
>>but i don't know how.
>>
>>sorry!
>
>
> I'm trying to assume that you're not here just to entertain or
> annoy us, so here's a seriously meant piece of advice: If you're
> going to ever learn programming (not to mention understand the
> underpinnings of lisp!), you need a minimum of mathematics.

i have enouth.

+ - * / exp root

>
> When you have that minimum knowledge, you'll know _several_
> reasons why 1 is the right value when you extend the expt-function
> from positive naturals (or reals) to naturals (or reals).

no i don't know.

and you don't know to explain me this.

i have to sleep know.

nested-macro is finished.

### Espen Vestre

Sep 17, 2002, 7:43:13 AM9/17/02
to
ilias <at_...@pontos.net> writes:
> > When you have that minimum knowledge, you'll know _several_
> > reasons why 1 is the right value when you extend the expt-function
> > from positive naturals (or reals) to naturals (or reals).
>
> no i don't know.

Then please go away (and take pick up your syntactic waste before

--
(espen)

### Thomas Stegen

Sep 17, 2002, 7:45:03 AM9/17/02
to

You can prove the following using mathematical induction,
I am not sure exactly how, and I am not about to try very
hard so if you want a rigid proof of thisa explanation a
book or websearch is in place.

(n > 0)
a^n = a * a * a * a ... * a (n times)
a^m = a * a * a * a ... * a (m times)

for example:

(a * a * a) / (a * a) = a

You see that the a's in the denomiator and numerator
cancel each other out. Suppose that. a^m is the
denomiator and a^n is the numerator; a^n / a^m. You see
that m a's will cancel out hence a^n / a^m = a^(n - m).

If you want proof, use mathematical induction or read a
book.

> and even if:
>
> isn't there a real-life-example for 2^0 = 1 ?

Espen Vestre provided one with apples and apple trees.

--
Thomas Stegen

Sep 17, 2002, 7:55:39 AM9/17/02
to
* Espen Vestre wrote:
> When you have that minimum knowledge, you'll know _several_
> reasons why 1 is the right value when you extend the expt-function
> from positive naturals (or reals) to naturals (or reals).

Who cares about reals? What we want is an explanation in terms of
counting oranges (or apples will do, bananas if pushed) of why
$e^{i\pi} = -1$. We demand complex fruit[1]!

--tim

Footnotes:
[1] since we seem to be dealing with a simple nut.

### Pascal Costanza

Sep 17, 2002, 8:31:19 AM9/17/02
to
> * Espen Vestre wrote:
>
>>When you have that minimum knowledge, you'll know _several_
>>reasons why 1 is the right value when you extend the expt-function
>>from positive naturals (or reals) to naturals (or reals).
>
>
> Who cares about reals? What we want is an explanation in terms of
> counting oranges (or apples will do, bananas if pushed) of why
> $e^{i\pi} = -1$. We demand complex fruit[1]!

You obviously don't have any clue about complex numbers, or about
complexity in general. It should be !e^{i\pi} = -1!, and not $e^{i\pi} = -1$. ! looks much nicer than $. I will shortly give a proof... Pascal P.S.: ;) -- Pascal Costanza University of Bonn mailto:cost...@web.de Institute of Computer Science III http://www.pascalcostanza.de Römerstr. 164, D-53117 Bonn (Germany) ### Jens Axel Søgaard unread, Sep 17, 2002, 8:44:18 AM9/17/02 to ilias wrote: > must cleanup my mind. > 2 exp 0 = 1 > > can anyone explain me this with apples? 2 ^ 3 means multiply with 2, do it 3 times. Thus 4 * 2 ^ 3 = 4 * 2 * 2 * 2 4 * 2 ^ 2 = 4 * 2 * 2 4 * 2 ^ 1 = 4 * 2 4 * 2 ^ 0 = 4 or 4 * 2^0 = 4 * 1 That is 2^0 = 1. -- Jens Axel Søgaard ### A. Polevitsky unread, Sep 17, 2002, 9:26:43 AM9/17/02 to Come on, Lispers! Don't you see? that this has been sent unto us for our sins: arrogance, verbiage, and lack of restraint. Repent and pray. ### Will Deakin unread, Sep 17, 2002, 9:36:58 AM9/17/02 to A. Polevitsky wrote: >Repent and pray. Yeth. Wepent and pway. ### Erik Naggum unread, Sep 17, 2002, 10:16:32 AM9/17/02 to * Tim Bradshaw | Who cares about reals? What we want is an explanation in terms of counting | oranges (or apples will do, bananas if pushed) of why$e^{i\pi} = -1$. We | demand complex fruit[1]! Various forms of consumer fruits are now marketed as "seedless". This is, of course, misleading. They really have imaginary seed. If you rotate a seedless fruit 90°, you get a fruitless seed. This can provide hours of fun. -- Erik Naggum, Oslo, Norway Act from reason, and failure makes you rethink and study harder. Act from faith, and failure makes you blame someone and push harder. ### Kenny Tilton unread, Sep 17, 2002, 10:18:12 AM9/17/02 to 2^1 => one dimension => line => two apples side-by-side forming a short, lumpy line. 2^2 => two dimensions => square => four apples touching arranged in a small, lumpy square 2^3 => three dimensions => cube => eight apples, one layer of four precariously balanced atop another. 2^0 => zero dimensions => point => one frickin' apple kenny clinisys ### Marco Antoniotti unread, Sep 17, 2002, 10:31:38 AM9/17/02 to ilias <at_...@pontos.net> writes: Suppose I put you an orange on the table. Now I ask you to demonstrate me that there is only a single orange on the table. Cheers -- Marco Antoniotti ======================================================== NYU Courant Bioinformatics Group tel. +1 - 212 - 998 3488 715 Broadway 10th Floor fax +1 - 212 - 995 4122 New York, NY 10003, USA http://bioinformatics.cat.nyu.edu "Hello New York! We'll do what we can!" Bill Murray in Ghostbusters'. ### Marco Antoniotti unread, Sep 17, 2002, 10:33:11 AM9/17/02 to polev...@pisem.net (A. Polevitsky) writes: > Come on, Lispers! Don't you see? that this has been sent unto us for > our sins: arrogance, verbiage, and lack of restraint. Repent and pray. You mean ilias' is Catholic? ### Christopher Browne unread, Sep 17, 2002, 10:42:20 AM9/17/02 to Tim Bradshaw <t...@cley.com> wrote: > * Thien-Thi Nguyen wrote: > >> (expt apple 0) => seed (of power). > > This is brilliant. Now I understand exponentiation. Thank you.[1] > > Could you please also explain the Hawking-Penrose collapse theorem in > terms of oranges? You see I only understand oranges, although I read > somewhere that oranges are not the only fruit and so I am more-or-less > comfortable with apples too. I would prefer you to stick to oranges > though. No. Only explain in terms of avocados. -- (concatenate 'string "cbbrowne" "@ntlug.org") http://cbbrowne.com/info/linuxdistributions.html "I think there's something to be said for a completely random user-interface policy - it keeps the users guessing, making life more interesting for people who deal with the casual X users. As for the screen display, at least you can't claim that people are mesmorized by sexy glitz which distracts them from the work at hand." -- Keith Packard ### Christopher Browne unread, Sep 17, 2002, 10:42:21 AM9/17/02 to Oh, no... "A dweem within a dweem, ow a nightmawe!!!" -- (concatenate 'string "cbbrowne" "@cbbrowne.com") http://cbbrowne.com/info/finances.html Rules of the Evil Overlord #139. "If I'm sitting in my camp, hear a twig snap, start to investigate, then encounter a small woodland creature, I will send out some scouts anyway just to be on the safe side. (If they disappear into the foliage, I will not send out another patrol; I will break out napalm and Agent Orange.)" <http://www.eviloverlord.com/> ### Erik Naggum unread, Sep 17, 2002, 1:10:00 PM9/17/02 to * Tim Brashaw | Could you please also explain the Hawking-Penrose collapse theorem in terms | of oranges? You see I only understand oranges, although I read somewhere | that oranges are not the only fruit and so I am more-or-less comfortable | with apples too. I would prefer you to stick to oranges though. * Christopher Browne | No. Only explain in terms of avocados. Ouch. That is such a harsh request. I think you will need approximately 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. ### Tim Bradshaw unread, Sep 17, 2002, 1:19:46 PM9/17/02 to * Erik Naggum wrote: > Ouch. That is such a harsh request. I think you will need approximately > 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. tsk, Erik, I expected better from you. That's the *Avogadro* number, often known as the bunch-of-grapes number. The *Avocado* number is 9.585138E22. --tim ### Mr. Poster unread, Sep 17, 2002, 1:22:55 PM9/17/02 to Erik Naggum wrote: > * Tim Brashaw > | Could you please also explain the Hawking-Penrose collapse theorem in terms > | of oranges? You see I only understand oranges, although I read somewhere > | that oranges are not the only fruit and so I am more-or-less comfortable > | with apples too. I would prefer you to stick to oranges though. > > * Christopher Browne > | No. Only explain in terms of avocados. > > Ouch. That is such a harsh request. I think you will need approximately > 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. > Effective only if each of the 6.02252E23 avocados falls on ilias's head - which nicely ties in with apple theory... ### Christopher Browne unread, Sep 17, 2002, 1:35:53 PM9/17/02 to The world rejoiced as Erik Naggum <er...@naggum.no> wrote: > * Tim Brashaw > | Could you please also explain the Hawking-Penrose collapse theorem in terms > | of oranges? You see I only understand oranges, although I read somewhere > | that oranges are not the only fruit and so I am more-or-less comfortable > | with apples too. I would prefer you to stick to oranges though. > > * Christopher Browne > | No. Only explain in terms of avocados. > > Ouch. That is such a harsh request. I think you will need approximately > 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. You should know by now how harsh I am. And you got the fourth decimal place wrong, too, in the avocado number. It is _not_ the same as Avogadro's Number. Come on, get it right, Eric! -- (reverse (concatenate 'string "moc.enworbbc@" "enworbbc")) http://cbbrowne.com/info/oses.html "Unless you used NetInfo. _Then_ changing network settings could often require torching of the existing system, salting of the ground it had rested on, and termination of anyone who used it." -- JFW <jwi...@biff.com> on comp.sys.next.advocacy ### Kaz Kylheku unread, Sep 17, 2002, 3:16:41 PM9/17/02 to Erik Naggum <er...@naggum.no> wrote in message news:<32412609...@naggum.no>... > * Tim Bradshaw > | Who cares about reals? What we want is an explanation in terms of counting > | oranges (or apples will do, bananas if pushed) of why$e^{i\pi} = -1$. We > | demand complex fruit[1]! > > Various forms of consumer fruits are now marketed as "seedless". This is, > of course, misleading. They really have imaginary seed. If you rotate a > seedless fruit 90°, you get a fruitless seed. This can provide hours of fun. I rather like this old joke: The number you have dialed is imaginary; please rotate your telephone ninety degrees and try again''. ;) ### Petr Swedock unread, Sep 17, 2002, 3:27:47 PM9/17/02 to Erik Naggum <er...@naggum.no> writes: > * Tim Brashaw > | Could you please also explain the Hawking-Penrose collapse theorem in terms > | of oranges? You see I only understand oranges, although I read somewhere > | that oranges are not the only fruit and so I am more-or-less comfortable > | with apples too. I would prefer you to stick to oranges though. > > * Christopher Browne > | No. Only explain in terms of avocados. > > Ouch. That is such a harsh request. I think you will need approximately > 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. Aha! Ilias is a mole! Peace, Petr ### Thomas F. Burdick unread, Sep 17, 2002, 5:01:14 PM9/17/02 to Erik Naggum <er...@naggum.no> writes: > * Tim Brashaw > | Could you please also explain the Hawking-Penrose collapse theorem in terms > | of oranges? You see I only understand oranges, although I read somewhere > | that oranges are not the only fruit and so I am more-or-less comfortable > | with apples too. I would prefer you to stick to oranges though. > > * Christopher Browne > | No. Only explain in terms of avocados. > > Ouch. That is such a harsh request. I think you will need approximately > 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. Yes, but I don't like moles, they scare me, so could you please avoid them in the proof? -- /|_ .-----------------------. ,' .\ / | No to Imperialist war | ,--' _,' | Wage class war! | / / -----------------------' ( -. | | ) | (-. '--.) . )----' ### Thomas F. Burdick unread, Sep 17, 2002, 5:19:27 PM9/17/02 to ilias <at_...@pontos.net> writes: > Espen Vestre wrote: > > > I'm trying to assume that you're not here just to entertain or > > annoy us, so here's a seriously meant piece of advice: If you're > > going to ever learn programming (not to mention understand the > > underpinnings of lisp!), you need a minimum of mathematics. > > i have enouth. > > + - * / exp root Okay, I know I shouldn't take Ilias seriously, but ... Programming takes a *lot* of math, if you want to be good at it. Your average production programmer *should* have a broader mathematical education than your average production chemist. This isn't true at the moment, and that's the cause of a fair amount of software problems and inefficiencies. However, all production programmers have at *least* a knowledge of middle-school math (by American standards). You're not even close. ### Christopher Browne unread, Sep 17, 2002, 5:25:33 PM9/17/02 to In the last exciting episode, t...@conquest.OCF.Berkeley.EDU (Thomas F. Burdick) wrote:: > Erik Naggum <er...@naggum.no> writes: > >> * Tim Brashaw >> | Could you please also explain the Hawking-Penrose collapse theorem in terms >> | of oranges? You see I only understand oranges, although I read somewhere >> | that oranges are not the only fruit and so I am more-or-less comfortable >> | with apples too. I would prefer you to stick to oranges though. >> >> * Christopher Browne >> | No. Only explain in terms of avocados. >> >> Ouch. That is such a harsh request. I think you will need approximately >> 6.02252E23 avocados to complete these proofs, a.k.a the avocado number. > > Yes, but I don't like moles, they scare me, so could you please avoid > them in the proof? That's very unfriendly of you. Why aren't you more gentle? Moles are nice creatures. And I can even prove it, based on the ANSI Lisp Standard. I'll be back soon with a set of macros to prove it, so long as you're gentle... -- (reverse (concatenate 'string "gro.mca@" "enworbbc")) http://cbbrowne.com/info/lsf.html Evil Overlords tend to get overthrown due to overly baroque plans with obvious fatal errors. Follow the "Rules of the Evil Overlord," and you need not fear heroic opposition, whether that hero be James Bond, Flash Gordon, or a little hobbit named Frodo. ### Thomas F. Burdick unread, Sep 17, 2002, 5:43:25 PM9/17/02 to Christopher Browne <cbbr...@acm.org> writes: > In the last exciting episode, t...@conquest.OCF.Berkeley.EDU (Thomas F. Burdick) wrote:: > > > Yes, but I don't like moles, they scare me, so could you please avoid > > them in the proof? > > That's very unfriendly of you. Why aren't you more gentle? > > Moles are nice creatures. Coming to the end of The Exponentiated Vegetable i just recognize some Violence. The Violence of The Mole. What does it violate? The Spirit of The Soil comming soon. ### Marc Spitzer unread, Sep 17, 2002, 5:49:28 PM9/17/02 to In article <xcvwupk1e...@conquest.OCF.Berkeley.EDU>, Thomas F. Burdick wrote: > Christopher Browne <cbbr...@acm.org> writes: > >> In the last exciting episode, t...@conquest.OCF.Berkeley.EDU >> (Thomas F. Burdick) wrote:: >> >> > Yes, but I don't like moles, they scare me, so could you please avoid >> > them in the proof? >> >> That's very unfriendly of you. Why aren't you more gentle? >> >> Moles are nice creatures. > > Coming to the end of The Exponentiated Vegetable i just recognize > some Violence. > > The Violence of The Mole. > > What does it violate? > > The Spirit of The Soil > > comming soon. Oh no, its spreading. some one call the CDC quick?!?!??! Christopher and Thomas, please step away from your computers, sit on your hands and wait for the nice men in the bubble suits to show up. marc ### Brad Miller unread, Sep 17, 2002, 7:09:35 PM9/17/02 to "Thomas F. Burdick" <t...@conquest.OCF.Berkeley.EDU> wrote in message news:xcvznug...@conquest.OCF.Berkeley.EDU... > ilias <at_...@pontos.net> writes: > > > Espen Vestre wrote: > > > > > I'm trying to assume that you're not here just to entertain or > > > annoy us, so here's a seriously meant piece of advice: If you're > > > going to ever learn programming (not to mention understand the > > > underpinnings of lisp!), you need a minimum of mathematics. > > > > i have enouth. > > > > + - * / exp root > > Okay, I know I shouldn't take Ilias seriously, but ... > > Programming takes a *lot* of math, if you want to be good at it. Your > average production programmer *should* have a broader mathematical > education than your average production chemist. This isn't true at > the moment, and that's the cause of a fair amount of software problems > and inefficiencies. Math is a formal system, and you should be good with reasoning over formal systems. I don't think there is a requirement for math per se; formal logic is probably better suited for most programming tasks. Philosophy is also very important since analysis is essentially the task of choosing a representational system which entails ontological commitments, making decisions as to how your software will garner data entailing epistemelogical tradeoffs etc. Personally, I don't deal much with sin and cos much, but "necessary that" and "possibly"; "forall" and "there exists"; "wants" and "believes" come up every day. ### Coby Beck unread, Sep 17, 2002, 7:31:38 PM9/17/02 to ilias wrote: > >>> can anyone explain me this with apples? to which "Kenny Tilton" <kti...@nyc.rr.com> replied: > 2^1 => one dimension => line => two apples side-by-side forming a short, > lumpy line. > > 2^2 => two dimensions => square => four apples touching arranged in a > small, lumpy square > > 2^3 => three dimensions => cube => eight apples, one layer of four > precariously balanced atop another. > > 2^0 => zero dimensions => point => one frickin' apple > Bravo! But will that explanation port to MacIntosh? ;) -- Coby Beck (remove #\Space "coby 101 @ bigpond . com") ### Erik Naggum unread, Sep 17, 2002, 8:58:33 PM9/17/02 to * Brad Miller | Math is a formal system No. Math is being able to see patterns and think in terms of abstractions that focus on the patterns and discard everything else. The result is a massive formal system that has grown in size and complexity with tremendous speed over the past 400 years or so. But mathematics starts with looking at a box of a dozen apples and see the number 12, at a crate of a dozen boxes and see the number 12, at a truck that holds a dozen crates and see the number 12, and then realize that there are 144 boxes and 1728 apples without ever counting to more than 12 because you worked this out by putting three matches each in three matchboxes, and then you repeated this thrice and put the three sets of three matchboxes aside and noticed that you had used up 27 matches and 9 matchboxes. Mathematics is watching something move at 1 foot per second and noticing that after 5 seconds, it had traveled 5 feet, then watching something accelerate at 1 foot per second per second and noticing that after 5 seconds, its speed was 5 feet per second and that it had traveled 12.5 feet and that in both cases the distance traveled was the area under the graph of its speed. Mathematics is noticing that two marbles can be laid out in two patterns, three marbles laid out in three times the two patterns of the two marbles and reason that the number of patterns is the product of all the whole numbers from 1 to the number of marbles. Mathematics is watching a yardstick rotate around one end to describe an area that is half as large as its circumference and that the relationship to the length of the yardstick is a constant that is present in circumferences, areas, and volumes of all things circular. If you think mathematics is only the formal system that describes these discoveries, you have missed out on all the exciting discoveries. | and you should be good with reasoning over formal systems. You should be good at finding the relevant and ignoring the irrelevant aspects of things that are vastly different, yet still similar in some ways. ### Christopher Browne unread, Sep 17, 2002, 10:20:06 PM9/17/02 to Oops! ma...@oscar.eng.cv.net (Marc Spitzer) was seen spray-painting on a wall: > In article <xcvwupk1e...@conquest.OCF.Berkeley.EDU>, > Thomas F. Burdick wrote: >> Christopher Browne <cbbr...@acm.org> writes: >> >>> In the last exciting episode, t...@conquest.OCF.Berkeley.EDU >>> (Thomas F. Burdick) wrote:: >>> >>> > Yes, but I don't like moles, they scare me, so could you please avoid >>> > them in the proof? >>> >>> That's very unfriendly of you. Why aren't you more gentle? >>> >>> Moles are nice creatures. >> >> Coming to the end of The Exponentiated Vegetable i just recognize >> some Violence. >> >> The Violence of The Mole. >> >> What does it violate? >> >> The Spirit of The Soil >> >> comming soon. > > Oh no, its spreading. some one call the CDC quick?!?!??! > > Christopher and Thomas, > > please step away from your computers, sit on your hands > and wait for the nice men in the bubble suits to show up. What I _really_ ought to do is to put together a collection of all the relevant postings to generate a "corpus," and run it through "parse-poetry.lisp". It can cope with both poetry (where line breaks are highly significant) and prose (where they aren't). It then basically builds Markov chains, a big hash table of how often various "substrings" of some specified length occur within the corpus. For instance, the above sentence breaks down to something like: (("the|corpus." . #<PSEQUENCE #x20381485>) ("within|the" . #<PSEQUENCE #x2037EBB9>) ("occur|within" . #<PSEQUENCE #x2037EB61>) ("length|occur" . #<PSEQUENCE #x2037EB09>) ("specified|length" . #<PSEQUENCE #x2037E875>) ("some|specified" . #<PSEQUENCE #x2037E811>) ("of|some" . #<PSEQUENCE #x2037E7A9>) ("\"substrings\"|of" . #<PSEQUENCE #x2037E751>) ("various|\"substrings\"" . #<PSEQUENCE #x2037E6F5>) ("often|various" . #<PSEQUENCE #x2037E681>) ("how|often" . #<PSEQUENCE #x2037E611>) ("of|how" . #<PSEQUENCE #x2037E5B5>) ("table|of" . #<PSEQUENCE #x2037E569>) ("hash|table" . #<PSEQUENCE #x2037E521>) ("big|hash" . #<PSEQUENCE #x2037E4D1>) ("a|big" . #<PSEQUENCE #x2037E481>) ("chains,|a" . #<PSEQUENCE #x2037E439>) ("Markov|chains," . #<PSEQUENCE #x2037E3ED>) ("builds|Markov" . #<PSEQUENCE #x2037E391>) ("basically|builds" . #<PSEQUENCE #x2037E32D>) ("then|basically" . #<PSEQUENCE #x2037E2C5>) ("It|then" . #<PSEQUENCE #x2037E25D>) ("###START###|It" . #<PSEQUENCE #x2037E205>)) where the PSEQUENCE objects contain a list of permissible successor words, and statistics of how often they occurred in the corpus. You can then go off and generate your own prose/poetry (as the case may be) by random selection, and produce a text with the same statistical characteristics as the corpus. Based on a corpus of poetry by a certain poet (who shall remain nameless, as he apparently monitors references to his name and plagues newsgroups where he gets referenced), this program generates the following: IN MUDDY FIELDS FORGOTTEN Above Muddy Fields Forgotten, O'er Fools Thrown There Astrew Raptors Soar So Patiently, For Soldier Meat Anew Their Caw A Certain Tempo, Eyes Glancing Down The Wait For Bullets Through Vacant Minds And Carrion For Their Plates. God! I Pray! Damn Such Fools! Such Brainless, Useless Twits! Send Them To A Special Hell! Where Together They Can Frit! About Their Flags And Colours, And Reasons Long Forgot! And Why They Died So Uselessly, Their Shrouded Faces Frought, With The Price Of Their Stupidity! And Their Crowns All Agilt! Axe Them All! The problem with the comp.lang.lisp "literary genius" is that it's a pain to collect corpus material. -- (concatenate 'string "chris" "@cbbrowne.com") http://www.ntlug.org/~cbbrowne/sap.html Dijkstra probably hates me (Linus Torvalds, in kernel/sched.c) ### Kaz Kylheku unread, Sep 17, 2002, 11:48:43 PM9/17/02 to In article <am64ua$j6h$1...@usenet.otenet.gr>, ilias wrote: > 2 exp 0 = 1 > > can anyone explain me this with apples? No; that requires highschool level mathematics. ### Marc Spitzer unread, Sep 17, 2002, 11:51:49 PM9/17/02 to In article <am8nsl$3olpe$1...@ID-125932.news.dfncis.de>, Christopher Browne wrote: > What I _really_ ought to do is to put together a collection of all the > relevant postings to generate a "corpus," and run it through > "parse-poetry.lisp". > for "he who must not be mentioned" would not "parse-drivel.lisp" be a better fit? No flippin way. I read that in jr. highschool(grades 7-9). I doubt yutz boy was around then the 20+ years ago. Thanks for posting it though I enjoyed reading it again. The sad part is that we are getting some first had experience with it again. marc ps It would be nice if we could figure out a way to make peace work better. ### Frank A. Adrian unread, Sep 18, 2002, 12:19:55 AM9/18/02 to ilias wrote: > you have confused me. > > i've requested an explanation based on apples. OK. You're an idiot. How do you like them apples? > to cleanup my mind. I'd learn Perl, instead. faa ### Frank A. Adrian unread, Sep 18, 2002, 12:23:43 AM9/18/02 to Thomas F. Burdick wrote: > What does it violate? > > The Spirit of The Soil No wonder you are trying to cleanup your mind... faa P.S. I've heard that, if you use certain readtables, mole can rhyme with trole, but only if 'l' and 'e' are equivalent. ### ilias unread, Sep 18, 2002, 12:21:16 AM9/18/02 to Espen Vestre wrote: > ilias <at_...@pontos.net> writes: > >>>When you have that minimum knowledge, you'll know _several_ >>>reasons why 1 is the right value when you extend the expt-function >>>from positive naturals (or reals) to naturals (or reals). >> >>no i don't know. > > Then please go away (and take pick up your syntactic waste before > you leave, please). > i extract: " the minimum knowledge for beeing in cll is knowing _several_ reasons why 1 is the right value when you extend the expt-function from positive naturals (or reals) to naturals (or reals). " "please go away..." rejected. ### ilias unread, Sep 18, 2002, 12:25:13 AM9/18/02 to Thomas F. Burdick wrote: > ilias <at_...@pontos.net> writes: ... >>i have enouth. >> >>+ - * / exp root > > Okay, I know I shouldn't take Ilias seriously, but ... > > Programming takes a *lot* of math, if you want to be good at it. Your > average production programmer *should* have a broader mathematical > education than your average production chemist. This isn't true at > the moment, and that's the cause of a fair amount of software problems > and inefficiencies. > > However, all production programmers have at *least* a knowledge of > middle-school math (by American standards). You're not even close. of course i'm not. and i don't want to be. ### ilias unread, Sep 18, 2002, 2:04:50 AM9/18/02 to Kenny Tilton wrote: > 2^1 => one dimension => line => two apples side-by-side forming a short, > lumpy line. > > 2^2 => two dimensions => square => four apples touching arranged in a > small, lumpy square > > 2^3 => three dimensions => cube => eight apples, one layer of four > precariously balanced atop another. > > 2^0 => zero dimensions => point => one frickin' apple ... >> i've requested an explanation based on apples. >> >> to cleanup my mind. zero apples any dimensions - still zero apples. one apple. 3 dimensions - still one apple. 2 dimensions - still one apple. 1 dimension - still one apple. 0 dimensions - still one apple 2 apples. 3 dimensions - 8 apples 2 dimensions - 4 apples 1 dimension - 2 apples 0 dimensions - 1 apple ( linguistic remark: notice: dimension_s_ ) 3 2 1 0 -------------- OO OOO OO OO O OO OO -------------- assimilation fault: zero dimensions = zero space zero dimensions = zero space ? Apples need space. Dimension 3, 2, 1 give space. Dimension 1 gives space as a line. The line has length, but now wideness and so no space. But the apples fit in the line. The space the apples need e.g. in dimension 1 is not given by the dimension-line itself. -- => OO | OO |-- => OO Thus 0-dimensions does not have to provide space for the apple, too. . => O The "0" in "0 dimensions" apply not to space. ... "2^0 = 1" assimilation passed. - You gave me the fundamental part to assimilate the construct "2^0 = 1" ! Thank you *very* much. ### ilias unread, Sep 18, 2002, 2:29:13 AM9/18/02 to many 'leg-pulls' here. hope you've fun. i had this time. could someone be so kindly to confirm the error in the specs i've found? this one about backquote-syntax i mean. in topic: am72i2$eov$1...@usenet.otenet.gr The Challenge of Nested Macros - [#V0.9] ### ilias unread, Sep 18, 2002, 2:36:28 AM9/18/02 to ilias wrote: > 2 exp 0 = 1 > > can anyone explain me this with apples? as the thread gets big. just for this is not missed: > Kenny Tilton wrote: > 2^1 => one dimension => line => two apples side-by-side forming a short, lumpy line. > > 2^2 => two dimensions => square => four apples touching arranged in a small, lumpy square > > 2^3 => three dimensions => cube => eight apples, one layer of four precariously balanced atop another. > > 2^0 => zero dimensions => point => one frickin' apple zero apples Apples need space. -- => OO | OO |-- => OO .. => O The "0" in "0 dimensions" apply not to space. .... ### Jacek Generowicz unread, Sep 18, 2002, 3:45:08 AM9/18/02 to Erik Naggum <er...@naggum.no> writes: [ ... Suggestions that observations of patterns are an essential part of mathematics ... ] > Mathematics is watching a yardstick rotate around one end to > describe an area that is half as large as its circumference ... and noticing that if you choose to call it a three-foot-stick the area is now one-and-a-half times as large as its circumference ? :-) (Not trying to detract from your general point at all here) ### Tim Bradshaw unread, Sep 18, 2002, 6:15:25 AM9/18/02 to * Erik Naggum wrote: > No. Math is being able to see patterns and think in terms of abstractions > that focus on the patterns and discard everything else. > [...] > If you think mathematics is only the formal system that describes > these discoveries, you have missed out on all the exciting > discoveries. Every CS graduate should have this tattooed onto their forehead. --tim ### Immanuel Litzroth unread, Sep 18, 2002, 7:28:14 AM9/18/02 to >>>>> "Erik" == Erik Naggum <er...@naggum.no> writes: Erik> * Brad Miller | Math is a formal system Erik> No. Math is being able to see patterns and think in terms Erik> of abstractions that focus on the patterns and discard Erik> everything else. Reading, or almost any task you accomplish that uses sensory input has this property. Erik> The result is a massive formal system that Erik> has grown in size and complexity with tremendous speed over Erik> the past 400 years or so. But mathematics starts with Erik> looking at a box of a dozen apples and see the number 12, at Erik> a crate of a dozen boxes and see the number 12, at a truck Erik> that holds a dozen crates and see the number 12, and then Erik> realize that there are 144 boxes and 1728 apples without Erik> ever counting to more than 12 because you worked this out by Erik> putting three matches each in three matchboxes, and then you Erik> repeated this thrice and put the three sets of three Erik> matchboxes aside and noticed that you had used up 27 matches Erik> and 9 matchboxes. Mathematics is watching something move at Erik> 1 foot per second and noticing that after 5 seconds, it had How do you watch something move at 1 foot per second? Most people would watch something move a certain distance during a certain interval and then calculate the average speed by division. But if you can watch speed, distance and timeinterval simultaneously the relation between them might have come as a suprise. Erik> traveled 5 feet, then watching something accelerate at 1 Erik> foot per second per second and noticing that after 5 Erik> seconds, its speed was 5 feet per second and that it had Erik> traveled 12.5 feet and that in both cases the distance Erik> traveled was the area under the graph of its speed. And you can watch accelerations too? Do you see forces? Erik> Mathematics is noticing that two marbles can be laid out in Erik> two patterns, three marbles laid out in three times the two Erik> patterns of the two marbles and reason that the number of Erik> patterns is the product of all the whole numbers from 1 to Erik> the number of marbles. Mathematics is watching a yardstick Erik> rotate around one end to describe an area that is half as Erik> large as its circumference and that the relationship to the Erik> length of the yardstick is a constant that is present in Erik> circumferences, areas, and volumes of all things circular. This is engineering. Mathematics is: given a (un)reasonable set of axioms can I prove that the this is a constant, or what happens if I take it as an axiom and use that, or what happens if I assume it is not a constant? Erik> If you think mathematics is only the formal system that Erik> describes these discoveries, you have missed out on all the Erik> exciting discoveries. I think you might have missed out on the most exiting discoveries if you think mathematics is a branch of experimental physics. Tell me: How many parallels to given line can you draw through a point? Have you observed the ratio or 2 to root(2) to be immesurable? How do you observe that a^x+b^x = c^z has no nonzero interger solutions for z > 2? The distinguishing feature of mathematics is the use of a formal system for reasoning even though the axioms in this system might not be in concordance with our perception. Immanuel ### Nils Goesche unread, Sep 18, 2002, 8:07:45 AM9/18/02 to Immanuel Litzroth <imma...@enfocus.be> writes: > >>>>> "Erik" == Erik Naggum <er...@naggum.no> writes: > > Erik> Mathematics is watching a yardstick rotate around one end > Erik> to describe an area that is half as large as its > Erik> circumference and that the relationship to the length of > Erik> the yardstick is a constant that is present in > Erik> circumferences, areas, and volumes of all things circular. > > This is engineering. Well, it's an _observation_. Just as `watching somebody move at 1 feet per second'' is an _observation_. Then comes abstraction and: > Mathematics is: given a (un)reasonable set of axioms can I prove > that the this is a constant, or what happens if I take it as an > axiom and use that, or what happens if I assume it is not a > constant? No. Even mathematicians have only a finite amount of time on their hands. They certainly do /not/ take any arbitrary set of axioms and see what they can prove with them. That's what it possibly appears to be at first sight, but it's not the whole story. There is always something that /motivates/ people to investigate /certain/ abstract systems but not others. Axiomatic formalism is the /technique/ used by mathematics, but not the whole thing. Even Bourbaki did /not/ just take any arbitrary axiomatic system and tried to prove as much as possible; they chose axiomatic systems that would finally be useful for finding answers to the /real interesting/ questions. > Erik> If you think mathematics is only the formal system that > Erik> describes these discoveries, you have missed out on all the > Erik> exciting discoveries. > > I think you might have missed out on the most exiting discoveries if > you think mathematics is a branch of experimental physics. Nonsense. All this has nothing to do with physics. Physics, among other fields, only gives rise to interesting abstractions which then motivate mathematicians to investigate them. > Tell me: How many parallels to given line can you draw through a > point? Have you observed the ratio or 2 to root(2) to be > immesurable? How do you observe that a^x+b^x = c^z has no nonzero > interger solutions for z > 2? By playing around with some numbers first? Planar geometry certainly was motivated by human observations of the real world. Then mathematicians tried to abstract out the key elements, which is not an entirely trivial matter, as it turned out, leading to projective and hyperbolic geometry, too. > The distinguishing feature of mathematics is the use of a formal > system for reasoning even though the axioms in this system might not > be in concordance with our perception. But the point is that they are not arbitrarily chosen, either. Regards, -- Nils Goesche "Don't ask for whom the <CTRL-G> tolls." PGP key ID 0x0655CFA0 ### Vassil Nikolov unread, Sep 18, 2002, 9:46:34 AM9/18/02 to Kaz Kylheku <k...@ashi.footprints.net> wrote in message news:<am8t2r$kc5\$1...@luna.vcn.bc.ca>...

An elementary school level treatment of apple arithmetics
can be found in (Lindgren, 1945). It does not assume any
prior knowledge or the possession of an apple computer.

References

Lindgren (1945)
Lindgren, Astrid. Pippi Långstrump. Raben & Sjogren, 1945.

---Vassil.

### Joe Marshall

Sep 18, 2002, 10:59:24 AM9/18/02
to

> Thomas F. Burdick wrote:
>
> > However, all production programmers have at *least* a knowledge of
> > middle-school math (by American standards). You're not even close.

ilias <at_...@pontos.net> writes:
> of course i'm not.
>
> and i don't want to be.

Ignorant! And proud of it!

### Erik Naggum

Sep 18, 2002, 10:59:43 AM9/18/02
to
* Immanuel Litzroth

| Reading, or almost any task you accomplish that uses sensory input has this
| property.

This is plainly false.

| How do you watch something move at 1 foot per second?

Sigh. Get the point already.

| And you can watch accelerations too? Do you see forces?

I can see the force of intelligence coming to get you.

| Mathematics is: given a (un)reasonable set of axioms can I prove that the
| this is a constant, or what happens if I take it as an axiom and use that,
| or what happens if I assume it is not a constant?

You have not understood mathematics. I recently discovered the works of
Keith Devlin, and would very strongly recommend his book «Mathematics: The
Science of Patterns: The Search for Order in Life, Mind and the Universe
(Scientific American Paperback Library)», ISBN 0-7167-6022-3. It may well
change the way you see mathematics. That would not be for the worse.

| I think you might have missed out on the most exiting discoveries if you
| think mathematics is a branch of experimental physics.

Good lord. How could you possibly have failed to see the point?

| The distinguishing feature of mathematics is the use of a formal system for
| reasoning even though the axioms in this system might not be in concordance
| with our perception.

This idiocy is why children do not learn mathematical thinking in "modern"
schools and why we have politicians, journalists, and social scientists who
suffer from what John Allen Paulos calls innumeracy. (Get some of his books,
too; he is a hilarious writer for thinkers. Start with «I Think, Therefore I
Laugh», then «Mathematics and Humor» and «A Mathematician Reads the
Newspaper». You need to get rid of the misconception that mathematics /is/
formal systems. It is like saying that poetry is an exercise in grammar.)

Speaking of books on mathematics, this is the book that led me to discover
Richard Courant: «What is Mathematics? An Elementary Approach to Ideas and
Methods ». It is a most spectacular work. The brilliance of Courant's mind
could not possibly fail to capture your fascination, if you have any.

### Espen Vestre

Sep 18, 2002, 11:13:48 AM9/18/02
to
Nils Goesche <car...@cartan.de> writes:

> > The distinguishing feature of mathematics is the use of a formal
> > system for reasoning even though the axioms in this system might not
> > be in concordance with our perception.
>
> But the point is that they are not arbitrarily chosen, either.

yes, but the initial intended application of new theories is often
purely "internal" to mathematics and very far from real-world
applications (but the nice thing is that the new theories may later
turn out to have "engineering" applications as well, I AFAIR
non-standard analysis is an example of this).
--
(espen)

### Nils Goesche

Sep 18, 2002, 11:29:14 AM9/18/02
to
Espen Vestre <espen@*do-not-spam-me*.vestre.net> writes:

Right. I think what Erik was describing was how new abstractions stem
from observation. Of course, what you observe is very often something
mathematical already, which gets then abstracted to greater heights;
but I don't think this changes the overall point.

### sv0f

Sep 18, 2002, 11:25:36 AM9/18/02
to
In article <32413499...@naggum.no>, Erik Naggum <er...@naggum.no> wrote:

> Speaking of books on mathematics, this is the book that led me to discover
> Richard Courant: «What is Mathematics? An Elementary Approach to Ideas and
> Methods ». It is a most spectacular work. The brilliance of Courant's mind
> could not possibly fail to capture your fascination, if you have any.

I recall reading an interview in "More Mathematical People" with
Herbert Robbins, co-author of "What is Mathematics?". In it,
he claims that he wrot the book and Courant, his superior, merely
stuck his name on it at the end. The book is at home; I will
try to look up the specifics of his allegation and post them
here. (A quick Google search turned up nothing relevant.)