RE: Flawed Science
Yes, yes, I did A level Maths and work in as a software developer now so I'm constantly dealing with numbers.
I understand what a series is, but we have to remember that a series (such as the one you demonstrated) only "tends" towards the resultant number (in this case 0.33333 recurring), it can never actually get to that result exactly;unless of course you take infinity as being that "special case" where it's beyond human comprehension and therefore the series is identical to the number. Having to consider things as "special cases" is just a flaw in mathematics again.It's an excuse or means of filling in the gaps where something has gone wrong in the reality of things.
I had a classic example the other day, when I was getting an Oracle database to generate me all of the whole hours between 2 date/time values.
When I got it to generate the hours between 16/10/2006 10:00 and 17/10/2006 06:00 (inclusive) it was giving me....
16/10/2006 10:00
16/10/2006 11:00
16/10/2006 12:00
.
.
17/10/2006 06:00
(21 rows)
But when I did the same for 16/10/2006 10:00 and 18/10/2006 06:00 I was expecting it to give me the extra 24 hours worth of rows of data i.e. 45 rows instead of 21.
Instead I got:-
16/10/2006 10:00
16/10/2006 11:00
16/10/2006 12:00
.
.
18/10/2006 05:00
(44 rows)
Further investigation showed that, the floating point processor in the computer had determined that the number of hours (inclusive) when I subtracted one date/time from the other came out as 44.9999999... (recurring) and so my database query that was applying a condition of something like (in english terms): rows <= (date2 - date1 inclusive) was not generating the 45th row because the calculation came out flawed.
I then found that this was "expected" behaviour, because of mathematics deeming that 44.999999... (recurring)is the same as 45. Just a shame that database queries work on real logic and can't take account of mathematical assumptions.
In the end I had to get thecomputer to simply round up the value to take account of this anomoly.
As far as normal calculations go, any tom, dick or harry can see that there are 45 inclusive hours between those two date/time values, but a) the computer can't calculate it correctly and b) mathematics says that it's not wrong that the computer is giving such a result.
Therefore, mathematics is stillflawed as I see it.
RE: Flawed Science
On the whole subject of flawed science there have been many debates on HP what? Evolution is one that springs to mind.
Taking the subject one level higher so to speak, is science itself less perfect or is it more flawed than it makes out? "Science" is supposed to be this pure scientific method and a search for truth. That's a purely theoretical construct which doesn't exist in the real world, though many aim at it. There are political issues and issues of personal bias - many issues of this nature.
You might find a scientific paper with findings and calculations that can't be flawed, and call that "perfect science". But who decided to do that study rather than another one? This decision propels investigation into one direction and possibly away from others. What important areas are not investigated because finance isn't there? Are many important findings and truths "filtered out" since they don't fit prevailing paradigms, and therefore are never published, the public not becoming aware of them?
The biggest flaws in science IMO are issues of this level or magnitude - that 'science' isn't what it makes out to be on many occasions. People being kicked out of their university posts (people I know) for not toeing the party line, etc., etc.
V
RE: Flawed Science
As far as I know they don't formalise mathematics until university. (I majored in maths and have a postgraduate degree in it, and we only formalised the algebra at uni). Not manymathematicians get toknow the precise axioms of mathematical groups, fields, and algebraic spaces until uni.
The point I was making is that the first line of the proof is equating a number x with a series which is formally meaningless. If you were to insert the limit notation, the line would simply read x = 1, and the rest of the algebra would go through as normal.
I am not saying that mathematics or science is perfect and I think it is extremely important to know that it isn't. I'm just saying that the particular example you cited doesn't demonstrate the argument. Anyway, enough about that from me. I'll be back with examples which I believe are questionable science.
Ooops. Forgot tolook intoyour database query...
People who program microchips are often not mathematicians. In this case it is the microchip programmer, not mathematics that is at fault. A chip cannot represent an infinite series and such an assumption is flawed, not the mathematics.
RE: Flawed Science
venetian
IMO spot on. I said the very same on another site.
RE: Flawed Science
While Science has overcome
the barriers of time,
distance and nationality,
it has done little
to promote
better understanding
between man and man,
nation and nation.
Sai Baba