I was going to post the following as Deep Thoughts XLIII, in a series of posts meant to be largely tautologous or at least trivial statements:
- Everyone older than you was once your age.
And then I realized that this is not actually a tautology. It might not even be true.
Suppose time is discrete in an Aristotelian way, so that the intervals between successive times are not always the same. Basically, the idea is that times are aligned with the endpoints of change, and these can happen at all sorts of seemingly random times, rather than at multiples of some interval. But in that case, (1) is likely false. For it is unlikely that the random-length intervals of time in someone else’s life are so coordinated with yours that the exact length of time that you have lived equals the sum of the lengths of intervals from the beginning to some point in the life of a specific other person.
Of course, on any version of the Aristotelian theory that fits with our observations, the intervals between times are very short, and so everyone older than you was once approximately your age.
One might try to replace (1) by:
- Everyone older than you was once younger than you are now.
But while (2) is nearly certainly true, it is still not a tautology. For if Alice has lived forever, then she’s older than you, but she was never younger than you are now! And while there probably are no individuals who are infinitely old (God is timelessly eternal), this fact is far from trivial.
3 comments:
Well, you can only have "successful and coherent deep thoughts" with at least coherent sentences.
A sentence like "Basically, the idea is that times are aligned with the endpoints of change, and these can happen at all sorts of seemingly random times, rather than at multiples of some interval." are not coherent. As such of course such "deep thoughts" will fail and be incoherent given such incohrent sentences.
So according to that incoherent sentence of yours "basically" "certain and specific times" occure at "noncertain and nonspecific times" - as far as I can tell.
Sure, so of course you can not measure any age accurately and precisely with such contradictory and incoherent assumptions of "having a certain and specific measure/metric of time" AND of "not having a certain and specific but a random measure/metric of time".
As such of course your "deep thoughts" are failing here.
By the way, what is the exact and precise change or rate of change of time or rather what is the time deriavtive of time [d/dt(t)=?!?] exactly and precisely and what does that exactly and precisely imply metaphysically?!?
An (easy) assignment for ChatGPT:
"Prove or disprove the statement and or claim of "Everyone older than you was once your age." by preassuming that d/dt(t)=1 and an or rather the ordinary metric and measure of time t in the 21st century.
Thank you."
ChatGPT's response:
"We are asked to prove or disprove the statement:
> “Everyone older than you was once your age,”
> under the assumptions that:
- Time t is measured with the ordinary metric used in the 21st century (i.e., linear and uniform time);
- d/dt(t) = 1 (i.e., time flows uniformly and smoothly).
---
📌 Interpretation of the Statement:
"Everyone older than you was once your age" — this means:
> For any person P whose age is greater than yours, there was a point in the past when P's age equaled yours.
Let’s formalize it slightly.
Let:
- t∈ℝ: time in years.
- t_you: your birth time.
- Let t_P: birth time of person P, who is older than you.
Because P is older than you, we assume:
t_P < t_you.
At any time t, your age is A_you(t) = t - t_you, and P's age is:
A_P(t) = t - t_P.
We are checking if for some time t*, A_P(t*) = A_you(t_now) — i.e., if P was once the age you are now.
That means:
t*-t_P = t_now-t_you ⇒ t* = t_now-t_you+t_P.
Is this a valid time? Let’s check:
- Since t_P < t_you, therefore t* < t_now.
- That means: there existed a time in the past when P was your current age.
---
✅ Conclusion: The Statement is TRUE
Under the assumptions that:
- Time is continuous and flows uniformly (as per d/dt(t) = 1),
- Time is measured linearly (as it is in 21st-century physics and clocks),
- Age is defined as the difference between current time and birth time,
Then any person older than you must have passed through all younger ages, including yours.
Thus, the statement:
> “Everyone older than you was once your age”
is true.
---
🚫 Caveats (Where It Could Be False)
- Different time metrics- (e.g. relativistic effects or subjective time perception) might violate this — but those are explicitly excluded by your assumption of ordinary 21st-century time.
- If someone died before reaching your age, they would not have been your age — but the statement refers only to living people older than you, or to their past existence, so this edge case can be sidestepped based on interpretation.
---
Let me know if you'd like to explore variations involving relativity or non-standard temporal models!"
Assigment and a question for Gemini:
"Please define exactly and precisely "metric space", "normed space" and "space with a measure" as shortly as possible. Also how would you currently describe sololy time (without physical space) regarding and considering those previously mentioned terms, "metric space", "normed space" and "space with a measure"?
Thank you."
Gemini's response:
"Here are the definitions:
- Metric Space: A set X with a function d: X×X → [0, ∞) (called a metric or distance function) such that for all x,y,z∈X:
1. d(x, y) = 0 ⇔ x = y
2. d(x, y) = d(y, x)
3. d(x, z) ≤ d(x, y)+d(y, z) (triangle inequality)
- Normed Space: A vector space V over ℝ or ℂ with a function ∥·∥: V → [0, ∞) (called a norm) such that for all x,y∈V and scalar α:
1. ∥x∥= 0 ⇔ x = 0
2. ∥α x∥ = |α| ∥x∥
3. ∥x+y∥ ≤ ∥x∥+∥y∥ (triangle inequality)
(Note: Every normed space is a metric space with d(x, y) = ∥x-y∥).
- Space with a Measure: A measurable space (X, A)$ (where X is a set and A is a σ-algebra on X) with a function μ: A → [0, ∞] (called a measure) such that:
1. μ(∅) = 0
2. For any countable collection of pairwise disjoint sets {E_i}(i=1→∞) in A, μ(∪(i=1→∞)(E_i)) = ∑(i=1→∞)(μ(E_i)) (countable additivity).
---
Now, describing time (without physical space) regarding these terms:
- Time as a Metric Space: Yes, time can be naturally described as a metric space. The set T = ℝ (representing the real number line for time) can be equipped with the standard metric d(t_1, t_2) = |t_1 - t_2|. This metric satisfies all the properties: the distance between two time points is zero if and only if they are the same, the distance is symmetric, and the triangle inequality holds.
- Time as a Normed Space: This is less straightforward and generally not how time is conceptualized in physics. A normed space requires an underlying vector space. While you can consider time differences as vectors (e.g., a duration of 5 seconds is a vector), defining a "zero vector" for time itself (a specific absolute origin) is problematic in a way that allows for arbitrary scaling and addition in the sense of a vector space where time points are the vectors. If you consider time intervals or durations as vectors, then the set of all possible durations could form a normed space, where the norm of a duration is simply its magnitude. However, time points themselves typically don't form a normed space.
- Time as a Space with a Measure: Yes, time can be very naturally described as a space with a measure. The set T = ℝ (or an interval of ℝ) can be endowed with the Borel σ-algebra B(ℝ) (the smallest σ-algebra containing all open intervals). The Lebesgue measure λ on (ℝ, B(ℝ)) then assigns a "length" or "duration" to subsets of time. For example, the measure of the interval [t_1, t_2] is λ([t_1, t_2]) = t_2 - t_1, which corresponds to the duration of that time interval. This is fundamental in many areas of physics and probability theory where events occur over time."
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