2024-02-11: Symbolic algebra and typing

2023-08-01: Population waves

2023-05-18: Math of telephone billing mystery

2023-05-05: Franklin and DNA More information…

2023-04-25: On angle and dimension

2023-02-20: On Leonardo da Vinci and Gravity

2022-04-29: Fabricating Evidence to catch Carmen Sandiego

2022-03-04: Probabilistic law of the excluded middle

2020-05-04: Archimedes and the sphere

2019-05-16: Glow worms return

2019-04-11: Original memetic sin

2019-01-31: The theory of weight

2018-11-06: Origins of telephone network theory

2018-10-24: Modern thought

2018-09-10: Feeding a controversy

2018-06-11: Glow worm distribution

2018-04-23: Outlawing risk

2017-08-22: A rebuttal on the beauty in applying math

2017-04-22: Free googles book library

2016-11-02: In search of Theodore von Karman

2016-09-25: Amath Timeline

2016-02-24: Math errors and risk reporting

2016-02-20: Apple VS FBI

2016-02-19: More Zika may be better than less

2016-02-17: Dependent Non-Commuting Random Variable Systems

2016-01-14: Life at the multifurcation

2015-09-28: AI ain't that smart

2015-06-24: Mathematical Epidemiology citation tree

2015-03-31: Too much STEM is bad

2015-03-24: Dawn of the CRISPR age

2015-02-12: A Comment on How Biased Dispersal can Preclude Competitive Exclusion

2015-02-09: Hamilton's selfish-herd paradox

2015-02-08: Risks and values of microparasite research

2014-11-10: Vaccine mandates and bioethics

2014-10-18: Ebola, travel, president

2014-10-17: Ebola comments

2014-10-12: Ebola numbers

2014-09-23: More stochastic than?

2014-08-17: Feynman's missing method for third-orders?

2014-07-31: CIA spies even on congress

2014-07-16: Rehm on vaccines

2014-06-21: Kurtosis, 4th order diffusion, and wave speed

2014-06-20: Random dispersal speeds invasions

2014-05-06: Preservation of information asymetry in Academia

2014-04-16: Dual numbers are really just calculus infinitessimals

2014-04-14: More on fairer markets

2014-03-18: It's a mad mad mad mad prisoner's dilemma

2014-03-05: Integration techniques: Fourier--Laplace Commutation

2014-02-25: Fiber-bundles for root-polishing in two dimensions

2014-02-17: Is life a simulation or a dream?

2014-01-30: PSU should be infosocialist

2014-01-12: The dark house of math

2014-01-11: Inconsistencies hinder pylab adoption

2013-12-24: Cuvier and the birth of extinction

2013-12-17: Risk Resonance

2013-12-15: The cult of the Levy flight

2013-12-09: 2013 Flu Shots at PSU

2013-12-02: Amazon sucker-punches 60 minutes

2013-11-26: Zombies are REAL, Dr. Tyson!

2013-11-22: Crying wolf over synthetic biology?

2013-11-21: Tilting Drake's Equation

2013-11-18: Why \(1^{\infty} eq 1\)

2013-11-15: Adobe leaks of PSU data + NSA success accounting

2013-11-14: 60 Minutes misreport on Benghazi

2013-11-11: Making fairer trading markets

2013-11-10: L'Hopital's Rule for Multidimensional Systems

2013-11-09: Using infinitessimals in vector calculus

2013-11-08: Functional Calculus

2013-11-03: Elementary mathematical theory of the health poverty trap

2013-11-02: Proof of the circle area formula using elementary methods

Tilting Drake's Equation

I was having a conversation with a friend about the likelihood of the existence of other forms of intelligent life out there. He was arguing that if life was out there, we'd have seen better evidence of it by now. I'd been thinking about related issues, but was more interested in the question of what conditions are really needed for the evolution of intelligent life on another planet. My proposal was then that we should all have our own competing versions of the Drake equation over which to argue. Here's my version.

First, I haven't been able to find any stories that describe a satisfactory form of life that doesn't originate as water+carbon based, so let's assume that's the kind life we're talking about.

We have good data now that planets are common -- as common as stars. 10's of billions ($10^{10}$).

$10^{-2}$ of those planets are in the habitable zone (rough guess)

There should be a factor for the planet being just the right size -- large enough to hold water down, but small enough that it's gravity well is easy to escape, but let's skip it and let the astronomers help out there.

All of these develop life (I think life is common on these planets with liquid water, though this is clearly a personal bias.)

Now, what's the chance life evolves to our level of complexity?

$10^{-3}$ because you need a crooked planet! Only on a planet with strong seasonality with fore-sight be evolutionarily beneficial. But too large a tilt could make the place un-inhabitable.

$10^{-3}$ because you need enough fossil fuel to provide a long window of opportunity during which interplanetary life is established, AND nuclear war is avoided.

That puts us at around $100$ space-faring civilizations in the galaxy (at a given time).

A tilt-term isn't in the original drake equation. One of the tasks implicit in the use of the Drake equation is to determine what conditions are necessary for the emergence of ``intelligent life'' from the primordial ooze. Defining ``intelligence'' or sapiency is perhaps a fool's errand -- Roadside Picnic and Solaris give good metaphors for the inherent challenges, and the Turing test we do have is so very disappointing. But even assuming we know ``intelligence'' when we see it, when can intelligence evolve? To me, intelligence is an ability to learn and plan ahead to deal with predictable changes in the world successfully. If your world never changes, there's no reason for intelligence. So,... intelligence will only appear on worlds that (1) possess stable tropical regions where life can get a foothold, and (2) other regions where large regular variations in which survival requires anticipation and preparation.

On our own planet, this has happened in three ways. First, earth rotates daily and always has (unlike mercury, for example). That's got to be pretty common, but we shouldn't forget it. Second, our moon drives mild ocean tides on a daily basis. This may have created the most important opportunities for the evolution of terrestrial vertabrate lifeforms. Third, earth is tilted relative to it's orbital plane around the sun. This probably happened during the earths creation billions of years ago. This creates seasons and the opportunity for complex terrestrial life-cycles that exploit annual variation in environment. So, at two important transitions complexity, earth has been special.

Once that leap to intelligent life happens, it seems trivial for some form of life to disperse through the galaxy, and we should be able to find evidence. This makes me think that rapid sublight traversal of the interstellar voids may be a much more hazardous undertaking than one might estimated at first pass.