Here is an example from cosmobiophysics. ))

Me: From the point of view of a microbiologist, the Hubble equation describes the expansion of the Universe as an exponential growth phase of a galaxy colony on a two-dimensional boundary surface of a dark nutrient medium. The colony grows by multiplying galaxies through binary fission. The specific growth rate of a galaxy colony is equal to the Hubble constant. The initial radius of the colony is equal to the radius of a Milky Way-type galaxy from which the colony began to grow. The number of galaxies currently observed is about 10^11.

Give a numerical estimate of the generation time (doubling time) of galaxies.

How will the speed of the colony front depend on the colony radius?

GPT-4: To estimate the generation time (doubling time) of galaxies, we need to use the relationship between the specific growth rate r and the doubling time Td in exponential growth. The specific growth rate is given by the Hubble constant H0.

Step 1: Relation Between Growth Rate and Doubling Time

The specific growth rate r is related to the doubling time Td by the following formula:

Td = ln(2) / r

Given that the specific growth rate r is equal to the Hubble constant H0, we can rewrite this as:

Td = ln(2) / H0

Step 2: Determine the Value of H0

The Hubble constant H0 is commonly expressed in units of km/s/Mpc. However, for this calculation, we need to convert it to units of s^{-1}.

A commonly accepted value for H0 is approximately: H0 ~ 70 km/s/Mpc

To convert H0 to s^{-1}:

1 Mpc (megaparsec) ~ 3.086*10^19 km

H0 ~ 70 km/s / 3.086*10^19 km ~ 2.27*10^{-18} s^{-1}

Step 3: Calculate the Doubling Time

Using the formula:

Td = ln(2) / H0

Td = ln(2) / 2.27*10^{-18} s}^{-1} ~ 3.05*10^17 s

Step 4: Convert the Doubling Time to More Convenient Units

Convert seconds to years:

year ~ 3.154*10^7 s

Td ~ 3.05*10^17 s / 3.154*10^7 s ~ 9.67*10^9 years

So, the generation time (doubling time) of galaxies is approximately 9.67*10^9 years.

Step 5: Speed of the Colony Front

The speed of the colony front v is related to the radius of the colony R and the specific growth rate r. For a colony growing exponentially, the speed at which the boundary expands is given by:

v = r*R

Since the specific growth rate r is equal to H0:

v = H0*R

Therefore, the speed of the colony front is directly proportional to the radius of the colony, with the proportionality constant being the Hubble constant.

In summary:

- The generation time (doubling time) of galaxies is approximately 9.67*10^9 years.

- The speed of the colony front depends linearly on the colony radius, with v = H0*R.

Me: these are my Q&A games with GPT-4o, - to find out the limits of its tolerance. A human cosmologist would simply not answer, - or would advise me to see a psychiatrist. But GPT-4o answered my questions quite correctly and without emotion, - showing that the microbial hypothesis explains the Hubble law no worse than the cosmological hypothesis about the expansion of the universe. And even predicts the intense birth of galaxies on the periphery of the visible universe.