It seems that some sections of academia are trying as hard as they can to make it a sin to make your own observations and form your own opinions of all the material available and weigh it up against what you see personally. -snip-
...No,... you believe your eyes and ears, and when the available reports don't match up with what you see evidence of, or, if you can find other reports that dispute it, you put it down to personal opinion. -snip-
...I'm one of those souls who likes to make his own mistakes, as generally I find they are far fewer and much less painful than those of others....- snip-
...is further convincing me that I'm right and always have been with the evidence available... -snip-
...You'll notice I have no self doubt, you can believe as you wish I have no desire to change your opinion. -snip-
So, from what I understand you feel that personal experience and observation of - this includes reading up on them - of events and facts around you are a base to evaluate the direction cause and effect are working and to base your beliefs and strategies on that.
This is very human (we do that everyday several times, making connections of facts we percieve and extrapolate from there to (gu)estimate outcomes of future scenarios) and it works most of the times fairly well:
If I run my car against a wall, it will break (and probably myself also); after about 5+ GF´s/Spousal Units you get the hang on where the problems will *always* come up/from; if I need 1 hour to walk 4 km, I will probably need about 2 hours for 8 klicks and can advise on my ETA, etc.
The problem is, our brain is *only* set to correctly estimate linear outcomes but completely fails in non-linear or exponential ones, for the simple physiological reason that we only have two eyes.
You can fairly accurately estimate distances to an object you see (the small distance between our eyes is enough to allow to triangulate sufficiently for our everyday use), but judging a height correctly is rather hard (thats why we aviators need the training on when to flare in landing, you can only drill it but not judge it): To establish the distance of a car, e.g., at 150 mtrs will reslult in only a slight error, but to tell when you are 150 mtrs high in the air is impossible w/o an altimeter, you might err up to 80% easily.
This phenomenon translates to all exponential evaluations, the estimation errors easily become too big to be allowable for daily life (hence we invented maths to *calculate* instead of having to estimate).
You can easily prove that to yourself holding on reading for a second and trying to make an educated
guess on the answers to the following questions (I will append the
calculated solutions at the bottom of this post). You will be surprised at how your estimation will fail by many factors the actual results (and just for the record I would love to hear what people reading those questions actually guess as answers):
a)
Estimate the total weight of 1000 steel balls of 1mm diameter
b)
Estimate the weight of a cork ball of 1 meter diameter
c)
Estimate how thick a newspaper page will become when you double it 50 times (actually, you can only double any paper 7 times in praxis, but lets for a moment assume we theoretically could double it 50 times)
Now, all natural developments are such exponential processes, following more or less the natural exponential function based on the "natural" logarithm (that is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828).
It applies to very different things like population growth, debt growth, investment results and plant growth alike and looks like the following if plotted to a graph:
Take for example mankind population growth:
It took roughly 5.000 yrs to reach the first billion in 1800, to reach the next it only took 130. The third billion was reached only 35 yrs later at 1960, and so on, to make it 4 more within 40 yrs to almost 7 billion now.
These nonlinear developments make it so hard to
estimate outcomes like global warming (or icing) effects as the effects of various factors combine.
From this POV I would think your "experience and perception" based method to evaluate where you will find yourself and your children at in 20 yrs time has the potential for serious error.
Now, add to this the problem that with all the various perceptions we make everyday (noise) it will be hard to filter out the ones to base your estimates on (signals) correctly (and the filtering process alone can be base to serious errors: Estimating the value of a parameter given no data may be an interesting problem in clairvoyance, but not in estimation theory), but this is probably for another thread and I wont discuss it here, also there exists enough material on the net for that as e.g. here:
http://cnx.org/content/m11263/latest/
My 2c,
Rattler
APPENDIX: Solutions to the estimation questions above
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a) 1000 steel balls of 1 mm diameter in total weigh aprox. 4 grams.
Calculation:
- The volume of a sphere is 4pi/3*r^3
- 1000 steel balls can be grouped in 10x10x10, more or less a cm3 on the outside and describing the sphere that is inside this cubic centimeter
- volume of a sphere inside 1 cm3 is roughly 0.52 cm3
- density of steel is approximately 7.8 grams/cm3, i.e. 0,52 cm3 weigh 4 grams roughly.
b) A ball of cork of 1m diameter weighs approximately 200 kilograms
This depends heavily on the type of cork you use, denisty of cork varies from 0.18 to 0.5 g/cm3, for the calculation I have taken 0.36
Calculation:
Volume of a sphere of 1 m3 (see formula above) is 0.52 m3, at the assumed density of 0.36 (i.e. 360 kg per m3) it pans out to 187 kg weight.
c)
A newspaper page doubled up 50 times will aquire a height of 1.03694111 × 10^15km = 1036941110 Million km = roughly
1 million times the distance Earth-Mars (at closest distance)
Caclulation:
- folding the newspaper page every time doubles its height
- doublling it 50 times this means you reach a height of 2^50 x the original thickness of the newspaper paper
- for the calculation I assumed this thickness to be 0.1mm = 0.0001m= 0.0000001 km
- 2^50 = 1.03694111 × 10^22, mutiply by 0.0000001 and you get 1.03694111 × 10^15 heigh in kilometers
Rattler
