Helio, you may have noticed that, as a chemical engineer, I have particularly advocated dimensional analysis. Your description is correct. Looking at the Drake Equation:

The Drake equation is:

{\displaystyle N=R_{*}\cdot f_{\mathrm {p} }\cdot n_{\mathrm {e} }\cdot f_{\mathrm {l} }\cdot f_{\mathrm {i} }\cdot f_{\mathrm {c} }\cdot L}

where:

*N* = the

**number of ****civilizations** in our galaxy with which communication might be possible (i.e. which are on our current past

light cone);

and

*R*∗ = the average

**rate** of

star formation in

our galaxy
*f*p = the fraction of those stars that have

planets
* n*e = the average number of planets that can potentially support

life per star that has planets

*f*l = the fraction of planets that could support life that actually develop life at some point

*f*i = the fraction of planets with life that actually go on to develop

intelligent life (civilizations)

*f*c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

*L* = the length of time for which such civilizations release detectable signals into space

[5][6]
Dimensionally: (where fraction is dimensionless)

number/time = (fraction)^4 multiplied by time x (number/star) x time

**My workings are:** 4 fractions Fractions are dimensionless as in number or stars with planets = number of stars (with planets) divided by total number of stars = number/number.

ne is number of planets per number of star that has planets = number/number.

These are all dimensionless.

R is rate or formation = number/time

L is time dimension (duration of signals).

Thus the result is

**Number** =

**number**/

*time* x

*time* = number.

Thus the equation is dimensionally correct.

However. that does not alter the fact that any such equation is only as good as its weakest link. Not one of these factors is known directly at present, and thus the Drake Equation has no validity whatsoever until all its components are known accurately. If all the components were to be accurately known bar one, and that one had a probability of being correct of 1 in a thousand, then the limit of accuracy of the equation would be 1 in a thousand, or 0.001.

Cat

P.S. If you take out the pure fractions, you are left with:

The average

**rate** of

star formation in

our galaxy **x** the length of time for which such civilizations release detectable signals into space.

I suggest that L is totally unknowable at the present time, and is likely to remain so in the indefinite future.

**We do not even know the answer for ourselves**. It might be 100 years or 10,000 years, or in the event of an asteroid impact it might be 6 months (fortunately unlikely).

It seems to me that there is no allowance in L for an asteroid impact. Unlikely though it may be, lack of allowance for this factor, all by itself, invalidates the whole equation in perpetuity.