> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

64/1 = 64
64/2 = 32
64/3 = 21 1/3
64/4 = 16
64/5 = 12 4/5
64/6 = 10 2/3
64/7 = 9 1/7
64/8 = 8
64/9 = 7 1/9
64/10 = 6 4/10
...

Nope, no discernable pattern at all
;)


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>> I love how the harmonics look like completely randomly chosen numbers,
>> with no obvious pattern at all.
>
> 64/1 = 64
> 64/2 = 32
> 64/3 = 21 1/3
> 64/4 = 16
> 64/5 = 12 4/5
> 64/6 = 10 2/3
> 64/7 = 9 1/7
> 64/8 = 8
> 64/9 = 7 1/9
> 64/10 = 6 4/10
> ...
>
> Nope, no discernable pattern at all ;)

Exactly. I mean, unless you happen to be able to compute 64/7 mentally, 
which normal humans can't.

If it was notated some other way, the pattern might be more obvious. But 
as it is...

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> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

Harmonics are integer multiple of the base frequency, or integer 
quotients of the base wave length having integer quotient of the power.

Armonic 1 is the base signal.
Armonic 2 have twice the frequency, or half the wave length, and half 
the amplitude. For 64, it gives 32.

Nothing random here, not even a bad pseudo-random. It's totaly 
deterministic.



Alain

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On 04/05/2011 00:21, Alain wrote:

> Nothing random here, not even a bad pseudo-random. It's totaly
> deterministic.

So is a psuedo-random number generator, and yet it still *looks* random.

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>>> I love how the harmonics look like completely randomly chosen numbers,
>>> with no obvious pattern at all.
>>
>> 64/1 = 64
>> 64/2 = 32
>> 64/3 = 21 1/3
>> 64/4 = 16
>> 64/5 = 12 4/5
>> 64/6 = 10 2/3
>> 64/7 = 9 1/7
>> 64/8 = 8
>> 64/9 = 7 1/9
>> 64/10 = 6 4/10
>> ...
>>
>> Nope, no discernable pattern at all ;)
>
> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
> which normal humans can't.

You're not that much younger than me, so maybe there's something 
fundamentally different between the school system in the UK vs. Canada, 
but in the 2nd or 3rd grade, we had to learn our multiplication tables 
by heart.

Normal humans should remember that 7 * 9 = 63.

Or if they don't, they should be able to guestimate that since 64 is 
rather close to 70, there's a good chance that 64/7 would be just a bit 
less than 70/7, which is easy to compute.

If not, I weep for humanity.

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>> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
>> which normal humans can't.
>
> You're not that much younger than me, so maybe there's something
> fundamentally different between the school system in the UK vs. Canada,
> but in the 2nd or 3rd grade, we had to learn our multiplication tables
> by heart.

This is almost universally regarded as one of the most useless things 
you learn in school. I haven't studied this statistically, but I suspect 
the majority of adults long since forgot all this stuff.

> Or if they don't, they should be able to guestimate that since 64 is
> rather close to 70, there's a good chance that 64/7 would be just a bit
> less than 70/7, which is easy to compute.
>
> If not, I weep for humanity.

Start weeping. This kind of reasoning is apparently far beyond the 
ability of most average people.

Even if it wasn't, standing there for five minutes computing tables 
isn't very immediate. If, instead of notating note pitches as 
wavelengths, they were noticed as, say "K * 7" or something, it would be 
far more instantly obvious what the relationship is, without having to 
perform complex mental arithmetic.

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On 04/05/2011 1:34 PM, Invisible wrote:
> This is almost universally regarded as one of the most useless things
> you learn in school. I haven't studied this statistically, but I suspect
> the majority of adults long since forgot all this stuff.

Rubbish! Maybe young adults can't remember them as they are over reliant 
on calculators.

-- 
Regards
     Stephen

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On 04/05/2011 06:05 PM, Stephen wrote:
> On 04/05/2011 1:34 PM, Invisible wrote:
>> This is almost universally regarded as one of the most useless things
>> you learn in school. I haven't studied this statistically, but I suspect
>> the majority of adults long since forgot all this stuff.
>
> Rubbish! Maybe young adults can't remember them as they are over reliant
> on calculators.




-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 4-5-2011 14:34, Invisible wrote:
>>> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
>>> which normal humans can't.
>>
>> You're not that much younger than me, so maybe there's something
>> fundamentally different between the school system in the UK vs. Canada,
>> but in the 2nd or 3rd grade, we had to learn our multiplication tables
>> by heart.
>
> This is almost universally regarded as one of the most useless things
> you learn in school. I haven't studied this statistically, but I suspect
> the majority of adults long since forgot all this stuff.

The whole point of learning multiplication tables by heart is that you 
need them to do all other computations in base 10.
If you don't know them by heart a large part of our culture is 
inaccessible to you.

>
>> Or if they don't, they should be able to guestimate that since 64 is
>> rather close to 70, there's a good chance that 64/7 would be just a bit
>> less than 70/7, which is easy to compute.
>>
>> If not, I weep for humanity.

I'll join you.

-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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On 24/05/2011 21:40, andrel wrote:

> The whole point of learning multiplication tables by heart is that you
> need them to do all other computations in base 10.

Most people would consider that you need a calculator to do any 
computations in base 10, beyond really trivial ones.

> If you don't know them by heart a large part of our culture is
> inaccessible to you.

Such as?

>>> If not, I weep for humanity.
>
> I'll join you.

I fear for the future of society, but for many reasons in addition to 
this...

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