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From: <jamikes.domain.name.hidden>

Date: Sat, 19 Aug 2006 15:13:33 -0400

Hi, Bruno

----- Original Message -----

From: "Bruno Marchal" <marchal.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Friday, August 18, 2006 11:23 AM

Subject: Re: ROADMAP (well, not yet really...

Bruno wrote:

Hi John,

Le 18-août-06, à 03:03, <jamikes.domain.name.hidden> a écrit :

*> Why has 6 'divisors'? because my math teacher said so?
*

then ...

*>Now I know you are joking. I know that you know that six has divisors.
*

It follows from the elementary definitions...<

[JM]:

Yes, I was. Not now: WHO supplied those "elementary definitions"?

Surely a math teacher or the ancestor of such. Not even Gauss was born with

the knowledge that 6/2=3.

*

Just as those "axioms" Stathis finds 'explanatory' stem from necessity to

hold a "theory" valid. Another view of the world would require different

"axioms".

*

Brent wrote about the crows who "counted" to 5, with some uncertainty even

higher and concluded that 'numbers exist in nature' - I did not examine what

the crows think, whether it was just a waiting period until their memory

expired, and the wise experimentors assigned it to 'counting' - all in their

human logic?

*

BTW I have a problem with the "perfect" 6:

ITS DIVISORS are 1,2,3,6, the sum of which is 12, not 6 and it looks that

there is NO other perfect number in this sense either.

(If 1 is a divisor - meaning 1x6 = 6 then 6 is also one: 6x1 = 6). An

exclusion of '1' would give a sum of 5 - Unless you want to exclude the

'number itself' from the "sum" - in which case the sum of "1" would be zero

(excluded the 1).

NOW I was joking.

John

I say to my students that in case they are saying a falsity (in math),

they will get a bad or a good note, depending on the way they will

defend the proposition. If they defend it by saying "because you say so

during the course", then they will get a *very* bad note, indeed!

Even, and I would say *especially* if it is true, that I have said that

falsity. Actually I teach like that, I make error all the time (mostly

intentionally but of course not always). It works. Students eventually

understand that they must understand math by themselves. Each year I

have student (about 20 years old) just realizing what math is all

about.

Now I know you are joking. I know that you know that six has divisors.

It follows from the elementary definitions. And I will not repeat them,

because that would be sort of an insult (of course a number is

"perfect" if it is equal to the sum of its proper divisors ... by

definition. Why using the word "perfect"? Pythagorean superstition or

folklore, but mathematicians are not sanguine about words and

representations. In the lobian interview all natural numbers are

represented by strings like 0, s(0), s(s(0)), s(s(s(0))), etc.

:-)

Best regards, bon week-end,

Bruno

http://iridia.ulb.ac.be/~marchal/

Date: Sat, 19 Aug 2006 15:13:33 -0400

Hi, Bruno

----- Original Message -----

From: "Bruno Marchal" <marchal.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Friday, August 18, 2006 11:23 AM

Subject: Re: ROADMAP (well, not yet really...

Bruno wrote:

Hi John,

Le 18-août-06, à 03:03, <jamikes.domain.name.hidden> a écrit :

then ...

It follows from the elementary definitions...<

[JM]:

Yes, I was. Not now: WHO supplied those "elementary definitions"?

Surely a math teacher or the ancestor of such. Not even Gauss was born with

the knowledge that 6/2=3.

*

Just as those "axioms" Stathis finds 'explanatory' stem from necessity to

hold a "theory" valid. Another view of the world would require different

"axioms".

*

Brent wrote about the crows who "counted" to 5, with some uncertainty even

higher and concluded that 'numbers exist in nature' - I did not examine what

the crows think, whether it was just a waiting period until their memory

expired, and the wise experimentors assigned it to 'counting' - all in their

human logic?

*

BTW I have a problem with the "perfect" 6:

ITS DIVISORS are 1,2,3,6, the sum of which is 12, not 6 and it looks that

there is NO other perfect number in this sense either.

(If 1 is a divisor - meaning 1x6 = 6 then 6 is also one: 6x1 = 6). An

exclusion of '1' would give a sum of 5 - Unless you want to exclude the

'number itself' from the "sum" - in which case the sum of "1" would be zero

(excluded the 1).

NOW I was joking.

John

I say to my students that in case they are saying a falsity (in math),

they will get a bad or a good note, depending on the way they will

defend the proposition. If they defend it by saying "because you say so

during the course", then they will get a *very* bad note, indeed!

Even, and I would say *especially* if it is true, that I have said that

falsity. Actually I teach like that, I make error all the time (mostly

intentionally but of course not always). It works. Students eventually

understand that they must understand math by themselves. Each year I

have student (about 20 years old) just realizing what math is all

about.

Now I know you are joking. I know that you know that six has divisors.

It follows from the elementary definitions. And I will not repeat them,

because that would be sort of an insult (of course a number is

"perfect" if it is equal to the sum of its proper divisors ... by

definition. Why using the word "perfect"? Pythagorean superstition or

folklore, but mathematicians are not sanguine about words and

representations. In the lobian interview all natural numbers are

represented by strings like 0, s(0), s(s(0)), s(s(s(0))), etc.

:-)

Best regards, bon week-end,

Bruno

http://iridia.ulb.ac.be/~marchal/

-- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.11.3/423 - Release Date: 08/18/06 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list.domain.name.hidden To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---Received on Sat Aug 19 2006 - 15:19:26 PDT

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