Is this not a proof of Fermat’s Last Theorem?

I’m wanted to play around with Fermat’s Last Theorem, and the proof seemed very obvious to me! Find the errors!

An + Bn ≠ Cn if A, B, C are whole numbers and n > 2.

Let’s try for a reductio ad absurdum. Let’s put Fermat’s claim in logarithmic form.

  1. loga X + logb Y = logc Z in which all terms equal n, n > 2.
  2. If a, b, and c are whole numbers all raised to the same power n then we can rewrite the above.
  3. (logc X / logc A) + (logc Y / logc B) = logc Z. Converting to the same base.
    1. Side notes:
    1. log5 9/ log5 3 + log5 16 / log5 4 = log5 25
    2. log5 (9/3 * 16/4) = log5 25
    3. logc (XY/AB) = logc Z
    1. (XY/AB) = Z
  4. (logc X / logc A) = (logc Y / logc B). Since all terms equal n.
  5. (logc X / logc A)/ (logc Y / logc B) = 1.
  6. (logc X / logc A) + (logc Y / logc B) = 2.

But we already said n > 2, thus logc Z cannot be greater than 2.

[Hahah! The errors here are super obvious!]

Is the Hybrid Model Good in itself?

What if the hybrid model forms on average more independent and dependable students?

What if the hybrid model provides the right balance of family and peer socialization?

What if the hybrid model wastes the least of amount of students’ time?

What if the hybrid model offers the same educational value as the best traditional schools at 60% the cost?

What if the hybrid model is best model of education for 50% of the school age population?

What if the hybrid model offers the optimum amount of flexibility and accountability for the average student?

What if the hybrid model is the model of education most fit for what the future will bring?

If even two of these are true, then the Hybrid Model is a great good.

Over 100 families have already chosen the hybrid model. It serves them well.

Dream of India

I had a dream that an Indian guy asked me for help navigating a futuristic city’s transportation system. Then he told me that the Indian languages near the border of China are the most interesting. I don’t know anything about Indian languages, so why did Prateek. I looked it up this morning to discover that northern Mishni is suspected to be a language isolate. He also had some choice words about the value of learning Mandarin.

The dream likely originates from a desire to visit India, a country I know little about, for two weeks.

Judging By Courses Taught

If I were placed in history entirely by what courses I taught each year I would be a different person. Consider the courses that this teacher marshaled on the field of battle last year: Latin, Geometry, Church History, Medieval History, Writing, Logic, Rhetoric. Why wasn’t I wearing one of these?

Sounds like a Late Medieval University Professor. I should have worn a robe and cap like so…
The different hats represent current grades – hair-net wearing ones being the ‘A students.’

This next year I am either moving into further into the future or deeper into the past. With Ancient History, Latin, Geometry, Morality, and Economics, I would think one of two things must be true. Either this person is a juggler fit for the circus, or he is literally from the school of Stoics.

Now the stoics had a great porch-game.
If I had a porch like this, darn right, I would have a lot of philosophical followers. We would play table tennis, offer libations, discuss the intricacies of corn-hole, and then test our theories with libations in one hand and a bag of potential life-giving seeds in the other. All in accord with the Logos.

But perhaps I am actually reenacting the life of someone at the other end of history, an Adam Smith who wrote on morality and economics and certainly knew his ancient history, or a statesman like John Stuart Mill, whose father forced him to learn Greek by age 12 and carved out from ancient philosophy and personal experience modern theories of liberty, economy, and ethics.
The Greek language was contained in that bump on his head. Greek is like that.

To follow in the footsteps of these greats is good, but to pass on the best that I have discovered in my own life to others is an honor. Perhaps laboring in the human flourishing mines is the best one can do.
“I loaded 16 tons of enriched Geometry, and what did I get?”

I get a lot out of it.