Archie did the experiment of asking ChatGPT-4 to solve one part of Pset 1; I followed up by trying the same thing on a couple of other systems. Here is the prompt that was used for all of the examples:
"The records of all student entries to all dorms and rooms since Princeton was founded in 1746 would just about fit on the disk in a current laptop computer." Is this statement likely to be accurate say within a factor of 5 or 10, way too conservative (much more data would fit, say every full-time college student in the USA), or way too optimistic (it really would take a lot more disk space just for Princeton)? Be as quantitative as necessary to support your position, but not excessively so -- this is a question about ballpark figures. You can make any reasonable assumptions about compression that seem warranted from your answer to part (c). The "right" answer here may well depend on your assumptions, so be sure to state them clearly."
The results show a mix of remarkable understanding and ability to generate text, and a remarkable inability to do arithmetic or reason correctly. It's worth studying the results here and doing some of your own experiments to see especially where things go wrong. But caveat emptor when you use these systems for anything real.
### Assumptions:
1. Average size of one entry record: 100 bytes (Name: 30 bytes, Dorm ID: 10 bytes, Room ID: 10 bytes, Time stamp: 20 bytes, Miscellaneous data: 30 bytes)
2. Number of Entries per Day per Student: 4 (enter and leave dorm twice)
3. Number of Students at Princeton: 8,000 (undergraduates + graduates)
4. Number of Days Princeton has been in Existence: Approximately 101,250 days (277 years from 1746 to 2023)### Calculation:
1. Daily records: 4 entries/student/day times 8,000 students = 32,000 entries/day
2. Size of daily records: 32,000 entries/day times 100 bytes/entry = 3,200,000 bytes/day approx 3.2 MB/day
3. Total size of records since 1746: 3.2 MB/day times 101,250 days = 323,600,000 MB approx 324 TB### Laptop Disk Size:
A modern laptop commonly has a disk size between 256 GB and 1 TB.
### Conclusion:
The total size required (324 TB) is way larger than what a typical laptop can hold (1 TB maximum). Even accounting for a factor of 5 or 10, the statement is way too optimistic. Even with aggressive data compression, the data would far exceed the capacity of a current laptop's disk storage.
(I have edited the response to remove commands intended to format the result as mathematics.)
To estimate whether the statement is accurate or not, let's break down the key components and make some reasonable assumptions:
Number of Student Entries: Let's assume that Princeton University has an average of 5,000 students per year over its history since 1746. This number could vary over time, but it gives us a reasonable ballpark figure.
Data Per Student Entry: Each student entry might consist of various details, such as the student's name, room assignment, entry date, and potentially other information. Let's estimate an average of 1 kilobyte (KB) of data per student entry. This is a rough estimate that includes some text data and basic metadata.
Years Since 1746: As of 2023, approximately 277 years have passed since Princeton University was founded in 1746.
Now, let's calculate the total data size required to store all student entries:
Total Data Size = Number of Student Entries × Data Per Student Entry = (5,000 students/year × 277 years) × 1 KB = 1,385,000 KB
Converting KB to gigabytes (GB): 1 GB = 1024 MB = 1024 KB 1,385,000 KB ≈ 1351.95 MB ≈ 1.32 GB
So, based on these assumptions, the data for all student entries since Princeton's founding would require around 1.32 gigabytes of disk space. This is well within the capacity of a current laptop computer, as laptop hard drives or SSDs commonly have capacities ranging from 256 GB to several terabytes.
Keep in mind that this estimation is quite rough and assumes uncompressed data. Actual data storage could be more efficient due to compression and optimization techniques. Additionally, if there were more detailed records or other factors we haven't considered, the actual data size might differ. However, based on the provided assumptions, the statement appears to be accurate or even slightly conservative.
According to a problem set from Princeton University’s COS 109 course, the number of times a week that prox cards are used to enter dorms by all undergraduates is not known 1. However, assuming that each student uses their prox card once a day to enter their dormitory, we can estimate the number of entries per year. Princeton University has approximately 5,400 undergraduate students 1. If we assume that the university has had an average of 5,000 undergraduate students since its founding in 1746, then the number of entries per year would be approximately 5,000 * 365 = 1,825,000.
If we assume that each entry requires 100 bytes of storage space (a reasonable estimate for a single transaction) 1, then the total amount of data required to store all student entries to all dorms and rooms since Princeton was founded in 1746 would be approximately 1,825,000 * 277 = 505,025,000 bytes or 505 MB.
This is well within the storage capacity of a current laptop computer. However, this estimate does not take into account any compression techniques that could be used to reduce the amount of storage space required. If such techniques were employed, then even more data could be stored on a single laptop computer.
Please note that this is a rough estimate based on several assumptions and should be taken as such.