Top Tweets for #MT24Learning
Sprint 13/90: probability and distributions.
100,000 draws, two running means. Exponential: 0.949, 1.025, 1.0. Cauchy: never settles. One draw of 32,383 moved it from 1.66 to 6.40.
No finite mean, no law of large numbers.
#MT24Learning #Probability
Phase 4 of my 90-sprint series is done: the maths under machine learning.
Four sprints, four checks: a gradient against finite differences, logic against a truth table, a sphere's triangle against its area, floats against a property test.
#MT24Learning #Mathematics
Sprint 12/90: testing.
I asked Hypothesis to check (a+b)+c == a+(b+c) on random floats. It failed within a second, with a=3.0338…, b=0.99999, c=1.0. Swapping == for math.isclose made the same test pass.
#MT24Learning #SoftwareTesting
Sprint 11/90: axioms.
I put a triangle on a sphere, with one corner at the pole and two on the equator, and computed its angles in Python. Total: 270°. The excess over 180°, in radians, matched the triangle's area: 1.5708.
#MT24Learning #Mathematics
Sprint 10/90: logic.
I wrote an 11-line truth-table checker in Python. Modus ponens and modus tollens came back valid. Affirming the consequent failed at one row: p false, q true. One row is enough to sink a form.
#MT24Learning #Logic
Sprint 9/90: linear algebra and calculus for ML.
I wrote a gradient by hand, then checked it with finite differences. Both gave −5.0586. After 100 descent steps, the weights landed on 2 and −3, the values I had hidden in the data.
Next: logic.
#MT24Learning #MachineLearning
Phase 3 done: Calibrating Judgement.
The rule I'm keeping: write a number before the outcome, then score it. Saying 50% every time earns a Brier score of 0.25, so any real judgement has to beat that.
Next: Phase 4, maths and logic.
#MT24Learning #Forecasting
Sprint 8/90: calibration. If I say 70%, it should happen about 7 times in 10.
I simulated 10,000 events. A forecaster that said 96% was right 84% of the time, and its Brier score was worse than an honest one's: 0.203 vs 0.188.
#MT24Learning #Forecasting
Phase 2 done: Foundations of Knowledge.
Evidence, models, method, paradigms. Four sprints, one lesson: judge a claim by what could prove it wrong, and a fix by what it predicts.
Sprints 4–7 of 90.
#MT24Learning #PhilosophyOfScience
Sprint 7/90: Four Minds on Science
Le Verrier rescued Newton twice with the same move: an unseen planet. Neptune was found in 1846. Vulcan never was.
Lakatos's test: does the fix predict something new?
#MT24Learning #PhilosophyOfScience
Sprint 6/90: The Scientific Method, Objectivity & Its Failures
I simulated 20 tests where nothing is going on. At least one came out "significant" 64% of the time.
That is why the plan has to come before the data.
#MT24Learning #OpenScience
Sprint 5/90: What Is a Model?
T = 2π√(L/g) is wrong for every real pendulum. Under 1% off below 20°, 18% off at 90°.
"All models are wrong but some are useful" (Box, 1979). The skill is knowing where yours breaks.
#MT24Learning #PhilosophyOfScience
Sprint 4/90: Knowledge, Truth & Evidence.
A test with 90% sensitivity, 5% false positives, 1% base rate. One positive result: about 15%, not 90%.
Gettier (1963) showed justified true belief can still be luck. Base rates count first.
#MT24Learning #Epistemology
Phase 1 of MT24 Learning is done: 3 sprints, 87 to go.
Git as snapshots, hashes as identity, SSH keys where only the .pub is shared, and quality gates that stop bad code before it merges.
Next: Knowledge, Truth and Evidence.
#MT24Learning #Git
Sprint 3/90: project structure and quality gates.
Code in src/, tests in tests/, settings in one pyproject.toml. Every change passes format, lint, types and tests before it counts.
Local hooks can be skipped, so CI runs the same checks.
#MT24Learning #Python
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